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XXIV NPCS MINSK-SOSNY 16-19MAY 2017
TOWARDS THEORY OF THE NEW SPIN STRUCTURESSergey Vladimirovich Smurov
Аlexandr Аlbertovich Maslikov
(Engineering Physics Institute Serpukhov)
Gennady Germanovich Volkov
Peterburg Institute of Nuclear Physics Gatchina
Engineering Physics Institute Serpukhov)
Tre-Neutrino Sull~Estensione
Multidimensionale Del Continuum
Spacio-Temporale Del`Universo Visible
MATTER IN VISIBLE IN UNIVERSE
1 Standard Model and new space-time geometrical structure
of the Universe
bull The geometrical basis of the modern quantum field theory sucessufullydescribing the
bull U(1)EM- electrodynamic processes the SU(3c)-gauge quantum chromodynamics and the
bull electroweak interactions based on the SU(2)WI times U(1)Y - gauge broken symmetry is our
bull space-time world what can be represented as a homogeneous and isotropic D = (3 + 1)-
bull four-dimensional continuum The symmetry properties of the spatial and temporal continuum
bull describe by the Lorentz-Poincaracutee groups and its representations and some fundamental
bull discrete symmetries- PTC
bull This space-time continuum can be immersed into
bull much huge comprehensive multidimensional world
bull The modern experimental data derived
bull from the elementary particle physics and astrophysics allow us to estimate the sizes
bull of the expanding visible part of the continuum
bull Λmin le Λ le Λmax
Space-time geometrical structureof the Universe
24052017
THE DOWN-UP QUARK MASSES
DEPEND ON THE E-M CHARGE
AND ON THE NUMBER OF GENERATIONS
( NEW CHARGE - ORIGIN FROM D=6)
THE FERMIONS MASSES AND W-Z- BOSONS
COULD
DEFINED BY THE E-W SCALE
M- EW-SCALE THE PHASE TRANSITION
BETWEEN TWO VACUUMS
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
Tre-Neutrino Sull~Estensione
Multidimensionale Del Continuum
Spacio-Temporale Del`Universo Visible
MATTER IN VISIBLE IN UNIVERSE
1 Standard Model and new space-time geometrical structure
of the Universe
bull The geometrical basis of the modern quantum field theory sucessufullydescribing the
bull U(1)EM- electrodynamic processes the SU(3c)-gauge quantum chromodynamics and the
bull electroweak interactions based on the SU(2)WI times U(1)Y - gauge broken symmetry is our
bull space-time world what can be represented as a homogeneous and isotropic D = (3 + 1)-
bull four-dimensional continuum The symmetry properties of the spatial and temporal continuum
bull describe by the Lorentz-Poincaracutee groups and its representations and some fundamental
bull discrete symmetries- PTC
bull This space-time continuum can be immersed into
bull much huge comprehensive multidimensional world
bull The modern experimental data derived
bull from the elementary particle physics and astrophysics allow us to estimate the sizes
bull of the expanding visible part of the continuum
bull Λmin le Λ le Λmax
Space-time geometrical structureof the Universe
24052017
THE DOWN-UP QUARK MASSES
DEPEND ON THE E-M CHARGE
AND ON THE NUMBER OF GENERATIONS
( NEW CHARGE - ORIGIN FROM D=6)
THE FERMIONS MASSES AND W-Z- BOSONS
COULD
DEFINED BY THE E-W SCALE
M- EW-SCALE THE PHASE TRANSITION
BETWEEN TWO VACUUMS
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
MATTER IN VISIBLE IN UNIVERSE
1 Standard Model and new space-time geometrical structure
of the Universe
bull The geometrical basis of the modern quantum field theory sucessufullydescribing the
bull U(1)EM- electrodynamic processes the SU(3c)-gauge quantum chromodynamics and the
bull electroweak interactions based on the SU(2)WI times U(1)Y - gauge broken symmetry is our
bull space-time world what can be represented as a homogeneous and isotropic D = (3 + 1)-
bull four-dimensional continuum The symmetry properties of the spatial and temporal continuum
bull describe by the Lorentz-Poincaracutee groups and its representations and some fundamental
bull discrete symmetries- PTC
bull This space-time continuum can be immersed into
bull much huge comprehensive multidimensional world
bull The modern experimental data derived
bull from the elementary particle physics and astrophysics allow us to estimate the sizes
bull of the expanding visible part of the continuum
bull Λmin le Λ le Λmax
Space-time geometrical structureof the Universe
24052017
THE DOWN-UP QUARK MASSES
DEPEND ON THE E-M CHARGE
AND ON THE NUMBER OF GENERATIONS
( NEW CHARGE - ORIGIN FROM D=6)
THE FERMIONS MASSES AND W-Z- BOSONS
COULD
DEFINED BY THE E-W SCALE
M- EW-SCALE THE PHASE TRANSITION
BETWEEN TWO VACUUMS
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
1 Standard Model and new space-time geometrical structure
of the Universe
bull The geometrical basis of the modern quantum field theory sucessufullydescribing the
bull U(1)EM- electrodynamic processes the SU(3c)-gauge quantum chromodynamics and the
bull electroweak interactions based on the SU(2)WI times U(1)Y - gauge broken symmetry is our
bull space-time world what can be represented as a homogeneous and isotropic D = (3 + 1)-
bull four-dimensional continuum The symmetry properties of the spatial and temporal continuum
bull describe by the Lorentz-Poincaracutee groups and its representations and some fundamental
bull discrete symmetries- PTC
bull This space-time continuum can be immersed into
bull much huge comprehensive multidimensional world
bull The modern experimental data derived
bull from the elementary particle physics and astrophysics allow us to estimate the sizes
bull of the expanding visible part of the continuum
bull Λmin le Λ le Λmax
Space-time geometrical structureof the Universe
24052017
THE DOWN-UP QUARK MASSES
DEPEND ON THE E-M CHARGE
AND ON THE NUMBER OF GENERATIONS
( NEW CHARGE - ORIGIN FROM D=6)
THE FERMIONS MASSES AND W-Z- BOSONS
COULD
DEFINED BY THE E-W SCALE
M- EW-SCALE THE PHASE TRANSITION
BETWEEN TWO VACUUMS
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull This space-time continuum can be immersed into
bull much huge comprehensive multidimensional world
bull The modern experimental data derived
bull from the elementary particle physics and astrophysics allow us to estimate the sizes
bull of the expanding visible part of the continuum
bull Λmin le Λ le Λmax
Space-time geometrical structureof the Universe
24052017
THE DOWN-UP QUARK MASSES
DEPEND ON THE E-M CHARGE
AND ON THE NUMBER OF GENERATIONS
( NEW CHARGE - ORIGIN FROM D=6)
THE FERMIONS MASSES AND W-Z- BOSONS
COULD
DEFINED BY THE E-W SCALE
M- EW-SCALE THE PHASE TRANSITION
BETWEEN TWO VACUUMS
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
THE DOWN-UP QUARK MASSES
DEPEND ON THE E-M CHARGE
AND ON THE NUMBER OF GENERATIONS
( NEW CHARGE - ORIGIN FROM D=6)
THE FERMIONS MASSES AND W-Z- BOSONS
COULD
DEFINED BY THE E-W SCALE
M- EW-SCALE THE PHASE TRANSITION
BETWEEN TWO VACUUMS
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
1967 ---------- 2017(STO-M(13))
bull WS-SU(2)XU(1)-Modelbull SU(5) and SO(10)mdashGUTbull Strings + Superstringsbull M11- Superrgravity+Kaluza-Klein
Compactificationsbull Heterotic SuperstringsE(8)XE(8) Models and
K6=CY_3- compactificationsbull 4-dim SS with WS Fermionsbull D-Membranesbull M11 M12 ndash and String Duality
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
ПУТИ РАСШИРЕНИЯ МЕТРИКИ
bull А) стандартный
bull Ds^2=dx_0^2-dx_1^2-dx_2-hellip-dx_n^2-
bull Lie algebras and groups SO(pq)n=p+q ndash space-time groups and double covered Spin(pq)hellip
bull B)Non-standard wayshellipT_mnkhellip
bull New symmetries -----gtnew groups and algebras theory of new numbershellip
bull New geometry- BCY_n Group algebra Spaceshellip
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
TOWARDS A N-aryMATHEMATICS+PHYSICS
bull THE WAYS TO EXTRA WORLD
bull 1)BCY- SU(n) G2 - Holonomy Geometry
bull 2)Theories of the Cyclic C_n- Complex Numbers
bull 3)Finite Group Algebras
bull MASS CHARGE SPIN hellip
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
BERGER-CALABI-YAU SPACES
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
K3-Manifolds ( BCY_2)
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
CY3-Newton polyhedron k=(11248)
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
МНОГОМЕРНОЕ РАСШИРЕНИЕ СПЕЦИАЛЬНОЙ ТЕОРИИ ОТНОСИТЕЛЬНОСТИ bull 1Принцип максимальности скорости света будет справедлив только для
заряженного вакуума то есть для частиц обладающих электромагнитным зарядом Темная материя и стерильное нейтрино Могут распространяться с гораздо большими скоростями
bull 2 Многомерное обобщение группы Лоренца предполагает существование другого буста и возможного раширения понятия времени даже за счет структуры
bull 3 принцип относительности также может потребовать расширения
За счет появления новых некомпактифицированых размерностей
стрелки времени или стрелки пространства Поэтому появляются несколько возможностей поиска параметра энергии ldquoветровойrdquoили ldquoтемпературнойrdquo от которой может зависеть скорость нейтрино и мы привели две схемы экспериментов- это должны решить будущие эксперименты
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
COMPLEXIFICATION OF R^n
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
GEOMETRY OF BINARY HYPER NUMBERS
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
N-ARY HYPER NUMBERS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
CONJUGATIONS CLASSESS AND ONE DIMENSIONAL REPRESENTATIONS
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
Ternary hyper-numbers
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
Ternary hyper-numbers
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
))((2
6
2
5
2
3
22
2
1
2
0 xxxxxx
)()( 5
2
3
2
2
2
1
2
0 xfxxxx
TOWARDS THE D+56- DIMENSIONAL EXTENSION
OF LORENTZ GROUP
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
R^n-COMPLEXIFICATION WITH FINITE GROUPS
Abelian Cyclic C _n- groups and Non-Abelian Groups
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull of light in Minkowsky (D = 3 + 1) space-time Absence of singularities in such a spacetimebull allows you to enter the gauge invariance in a region which can connect two kinds ofbull matter the matter substance and radiation The substance described by the fundamentalbull fermion fields with spin 12[4] GWeyl[11] and radiation - gauge fields with spin 1 Thebull question of maintaining gauge invariance may depend on the existence of singularities inbull this space-time which can be a source of symmetry breaking This option is actuallybull a violation of gauge symmetry associated with the existence of space-time singularitiesbull at small or large distances Note that the existence of singularities at small distancesbull can lead to a change of the Riemann metric and therefore to a dynamical violation ofbull space-time Lorentz symmetry ( see for example [7])
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull Thus the formalism of quantum field theory includes the geometric foundationbull of space-time picture of the rdquovisible rdquoworld and the operator-functional methods of describingbull a matter moving and interacting in this environment But now some phenomenabull in physics of elementary particles pose the question the need to expand our notions ofbull space and time In this case the first question arises of dimension and signature of abull new hypothetical world In our opinion now modern science close to understanding tobull the origin of the visible part of universe defined by a D=(3+1)-dimensional space-timebull continuum obeying to the laws of absolutism speed of light and the observable fermionbull matter of which has the rdquounifiedrdquo electromagnetic nature In articles [2] [19] it wasbull suggested that only the Dirac fermion matter can satisfy to the laws of absolutism speed
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
LIE algebras SO(31) and SL(2C)
bull The Lie algebra of Lorentz group SO(3 1) is isomorphic to the algebra of its double covering
bull Spin(3 1) = SL(2C)-groupbull the irreducible representations of what canbull be defined by two integer or semi-integer numbers (μ ν) of the
finite-dimensional representations of the SU(2) timesSU(2) groupbull The minimal representations of this group arebull Scalar (0 0) representation bull Weyl spinors (12 0)L- and (0 12)R-representations bull what are related by P -parity operation (and complex conjugation)
bull x0 rarr x0 x rarr -x (12 0) rarr (0 12)
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
НАЧАЛО SU(2)_SWxU(1)_Y
bull To describe the I_- charged weak currentsbull and combine them to the EM- currents in Weinberg-Salam
model SU(2)WI times U(1)Y itbull was used the ideas of the Heisenberg SU(2)I - isotopic group
and the following relation
bull Q(EM) = I_3 + Y2
bull As one of the main result of a such model it was predicted the neutralbull weak interactions what was experimentally confirmed in GARGAMELLE CERN neutrinobull experiments in 1974 year In this model the P- violation (C-violation) was constructed bybull hands taking the left- and right handed fermions in different SU(2)WI - representationsbull For breaking the gauge symmetry in Weinberg- Salam model it was used the mechanismbull in the internal sector of the model what predicted the existence of a new fundamentalbull scalar particle- Higgs boson
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull Mechanism of the appearance ofbull the masses of gauge bosons and fermions is enough
formal and it is not clear its link tobull structural changes of the space-time At least in spite
of preliminary of strong indicationsbull and a lot of discussions CERN plans to continue these
experiments for the future cyclebull of LHC-collider work with planing to get much more
the energy of the proton beamsbull Fermilab also resumed the work on the improvement
of the Tevatron to finally clarify the
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull nature of signals detected at CERN collider at energy of 125 Gev One can propose thatbull the role of the weak sector of the Standard Model is the way to understand the originbull of the visible universe More suppressed processes going to the CP- violation may bebull associated with an unknown dynamics at the more smaller distances sim 10104857616104857617cm Inbull addressing this issue again we faced with the dilemma of the mechanism of these phenomenabull defects of the space-time geometry orand a new dynamics related to the newbull interactions Obviously the issue is closely related to another important problem - thebull existence of three quark-lepton families All experimental information on three familybull mixing and CP-violation can be encoded into the Cabibbo-Kobajashi-Maskawa (CKM)-bull matrix parameters which also requires explanation
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull The 3- family mixing explanation is
bull completely going into the mass origin problem In the second case one should again to
bull study the problem related to the local gauge symmetry breaking - rdquoHiggsologyrdquo or unknown
bull a space-time singularity structure In the depths of this phenomenology is waiting
bull for us very rich physics what can shed light on the production the visible part of Universe
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
Towards a new spinor-fermion
structurebull we do not define the fermion matter that fills the
space-time continuum should have a universal property ie Dirac half-one fermions[2]
bull [GV][AV] bull It means that we can imagine the existence of exotic
fermion matter for example bull having another spin 1n n ge 3 and without an
electromagnetic (color) chargebull nature In this picture our visible Dirac Universe
forming a topological cycle could bebull embedded into Meta - Universe having much more
reach the space-time topology
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull As abull messenger between the cycles we suggested neutrinos with Dirac mass equal to zerobull To construct the spin 1n fermion theories first one should find out the examples ofbull the geometrical spaces having such a spinor structure [19][20][22] Taking into accountbull a possibility to imply the spaces with arbitrary spin structure in formulation of the basicbull principles of the string theory one could significantly expand the assumption touchingbull the D- dimensional pseudo-Lorentz space in which the string is moving We think thatbull in this case the string and superstrings theories could considerably extend the set ofbull predictions for modern physics of elementary particles In according to such geometricalbull objects one can search for new symmetries what we already started to study in the classbull of n-ary symmetries with corresponding n-ary algebras what already have been discussedbull in literature for example [6][22] and reference there
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
РАСШИРЕНИЕ СИММЕТРИИ ЛОРЕНЦА
bull
bull 119878119894 119878119895 = 119894120576119894119895119896119878119896 1205901198942 = 12 = 1205900
bull 119878119895 =1
2120590119895 119895 = 123
bull 1205900 =1 00 1
1205901 =0 11 0
1205901 =0 minus119894119894 0
1205903 =1 00 minus1
bull 119876119886 119876119887 = 0 1198761198863 = 13 = 1198760
bull
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
GROUP ALGEBRAS -GEOMETRY
bull 120556119894119886 = 119878119894 otimes 119876119886 =1
2120590119894 otimes 119876119886 i=0123a=012
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888bull
bull 120556 =
1
2
1199090 + 1199093 1199100 1199090 + 1199093 1199101 1199090 + 1199093 1199102
1199090 + 1199093 1199102 1199090 + 1199093 1199100 1199090 + 1199093 1199101
1199090 + 1199093 1199101 1199090 + 1199093 1199102 1199090 + 1199093 1199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
1199090 minus 1199093 1199100 1199090 minus 1199093 1199101 1199090 minus 1199093 1199102
1199090 minus 1199093 1199102 1199090 minus 1199093 1199100 1199090 minus 1199093 1199101
1199090 minus 1199093 1199101 1199090 minus 1199093 1199102 1199090 minus 1199093 1199100
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896
bull = 119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull 120556119886119894119879 = 119876119886 otimes 119878119894 = 119876119886 otimes
1
2120590119894
i=0123a=012
bull 1198760 =1 0 00 1 00 0 1
1198761 =0 1 00 0 11 0 0
1198762 =0 0 11 0 00 1 0
bull 120556119879 = 119888=02 119910119888119876119888 otimes 119896=0
119896=3 119909119896119878119896 =
119888=02 119910119888119876119888 otimes
1
2 119894=0
3 119909119894120590119894
GROUP ALGEBRAS -GEOMETRY
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull
bull 120556119879(119878119880(2119876) =1
2
1199100 1199101 1199102
1199102 1199100 1199101
1199101 1199102 1199100
otimes1199093 1199091 minus 1198941199092
1199091 + 1198941199092 minus1199093=
bull
bull =1
2
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199101 (1199091minus1198941199092)1199101
(1199091 + 1198941199092)1199101 minus11990931199101
11990931199102 (1199091minus1198941199092)1199102
(1199091 + 1198941199092)1199102 minus11990931199102
11990931199100 (1199091minus1198941199092)1199100
(1199091 + 1198941199092)1199100 minus11990931199100
GROUP ALGEBRAS -GEOMETRY
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
SU(2Q)-ALGEBRA
bull 120556 = 119896=0119896=3 119909119896119878119896 otimes 119888=0
2 119910119888119876119888
bull
bull 120556119894119886 120556119895119887 = 119894120576119894119895119896120578119888120556119896119888
bull 120556119896119888 = 119878119896 otimes 119876119888 119876119888 = 119876119886119876119887 = 120578119886119887119888119876119888
bull 119878119894 otimes 119876119886 119878119895 otimes 119876119887 = 119878119894 ∙ 119878119895 otimes 119876119886 ∙ 119876119887 minus 119878119895 ∙
119878119894 otimes 119876119887 ∙ 119876119886 = 119878119894 ∙ 119878119895 minus 119878119895 ∙ 119878119894 otimes 119876119886119876119887 =
bull = 119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888 = 119894120576119894119895119896119878119896 otimes 119876119886119876119887 =
119894120576119894119895119896119878119896 otimes 120578119886119887119888119876119888
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull 120556(119878119880(2119876)) =
1
2
11990931199100 11990931199101 11990931199102
11990931199102 11990931199100 11990931199101
11990931199101 11990931199102 11990931199100
1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102
1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100 1199091 minus 1198941199092 1199101
1199091 minus 1198941199092 1199101 1199091 minus 1198941199092 1199102 1199091 minus 1198941199092 1199100
1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102
1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100 1199091 + 1198941199092 1199101
1199091 + 1198941199092 1199101 1199091 + 1198941199092 1199102 1199091 + 1198941199092 1199100
minus11990931199100 minus11990931199101 minus11990931199102
minus11990931199102 minus11990931199100 minus11990931199101
minus11990931199101 minus11990931199102 minus11990931199100
bull
SU(2Q)-ALGEBRA
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
SU(3^c)XU(1)XSU(2)XU(1)xSU(3H)XU(1H)4-dimsuperstrings
With World-Sheet Fermions(1992Padova)
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
1999-2000-Padova-CERN
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
СВОЙСТВА НЕЙТРИНО О МНОГОМЕРНОМ ОБОБЩЕНИИ ТЕОРИИ ОТНОСИТЕЛБНОСТИ
ПРЕДСТАВЛЕНИЯ ГРУППЫ ЛОРЕНЦ- ПУАНКАРЕ
bull 1 Спин s=frac12
bull 2 Майорано-Вейлевская природа - 2-х компклексные степени свободы
3 Масса m =O(eV)
ЭЛЕКТРОМАГНИТНАЯ СТЕРИЛЬНОСТЬ bull 4 Заряд Q (EM)= O
bull 5 Магнитный момент Mag=O(0)
(V ndash A )- СЛАБАЯ СВЯЗЬ С ЗЛЕКТРОМАГНИТНЫМ МИРОМ
bull 6 Взаимодействие слабое
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
24052017
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull Referencesbull [1] ANAmaglobeli ARKereselidze AGLipartelianiGGVolkov The
supersymmetricbull vector-like horizontal model with intermediate symmetry breaking
scale Phys Lett B237bull (1990) 417bull 263bull Alexander Maslikov and Guennady Volkovbull [2] V Ammosov G Volkov Can Neutrinos Probe Extra Dimensions
hep-ph0008032 Paduabull preprint DFPD-00TH39 arXivhep-ph0008032v1 (2000)bull [3] DS Baranov and GGVolkov Neutrino and Extra World
arXiv12114708bull rdquoNeutrino On The Possible New Time Structurerdquo arXiv13021482
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull [6] ADubrovskiy and GVolkov Ternary numbers and algebras Reflexive numbers and Bergerbull graphs AdvApplCliffordAlgebras17159-1812007bull archivhep-th0608073 (2006)bull [7] J R Ellis N E Mavromatos D V Nanopoulos and G Volkov Gravitational-Recoil Effectsbull on Fermion Propagation in Space-Time Foam Gen Rel Grav 32 (2000)1777 [arXivgrqcbull 9911055]bull [8] RW Hamilton On Quaternions Proceedings of the Royal Irish Academy Nov11 (1844)bull v3 (1847) 1-16bull [9] LN Lipatov A Sabio-Vera VN Velizhanin and GG Volkov From New Geometry Towardsbull a New Symmetry Reflexive Numbers and Berger Graphs from Calabi-Yau Spacesbull Dark Matter in Astro- and Particle Physics DARK-2004 Springer (2004) 622-655 ISBN-bull 13 978-3-540-26372-2 Springer Berlin Heidelberg New York IntJModPhys A21 (2006)bull 2953-3006bull [10] L N Lipatov M Rausch de Traunbenberg G Volkov On the ternary complex analysisbull and its applications J Math Phys 49 013502 (2008)
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
bull [14] V Monich B Struminsky G Volkov Oscillation and CP violation in the ldquohorizontalrdquobull superweak gauge scheme Phys LettB104 p 382-384(1981)bull [15] H Poincarґe Sur les propriґetґes du potential et sur les fonctions Abeliennes Acta Matematicabull 22(1) 89-178bull [16] V Samoylenko and GVolkov The GUT of the light On the Abelian Complexifications ofbull the Euclidean Rn spaces arXiv09122037 (2009)bull [17] GG Volkov AG Liparteliani VA Monich YP Nikitin Mixing of leptons with differentbull quantum numbers in gauge schemes of the weak and electromagnetic interactions Sov Jbull Nucl Phys (Engl Transl) 27(1978)735bull YadFiz 27 (1978) 1395-1402 preprint IFVE-77-89bull [18] G Volkov Hunting for the New Symmetries in Calabi-Yau Jungles IntJ Mod Phys A19bull (2004) 4835-4860 hep-th0402042bull [19] GG Volkov Annales Fond Broiglie 31 (2006) 227bull Geometry of Majorana neutrino and new symmetriesbull short version in hep-ph0607334bull [20] G Volkov The possible signals from D=6 arxiv11123583(2011)bull [21] G Volkov On the complexifications of the Euclidean Rn spaces and the n-dimensionalbull generalization of Pythagore theorem arXiv10065630(2010)bull [22] G Volkov Ternary rdquoQuaternionsrdquo and Ternary TU(3) algebra arXiv10065627 (2010)bull 264
