Bibliography

The following list is not exhaustive but is intended to offer the reader a set of writings complementary to this work.

General References

Quantum Mechanics

L. D. LANDAU, E. M. LIFCHITZ, Quantum Mechanics, Pergamon Press, 1962. E. MERZBACHER, Quantum mechanics, Wiley, 1970 (2nd edition). S. GASIOROWICZ, Quantum physics, Wiley, 1974. A. MESSIAH, Quantum mechanics (2 vol.), North-Holland, 1976. C. PIRON, Mecanique quantique, Presses poly techniques et universitaires ro­mandes, Lausanne, 1990. J. J. SAKURAI, Modern quantum mechanics, Revised edition, Addison­Wesley, 1994. C. COHEN-TANNOUDJI, B. DIU, F. LALOE, Quantum mechanics (2 vol.) , Wiley, 1997.

Many-Body Problems

J. J. THOULESS, The quantum mechanics of many-body systems, Academic Press, 1961. P. NOZIERES, Le probleme aN-corps, Dunod, 1963. N. H. MARCH, W. H. YOUNG, S. SAMPANTHAR, The many-body problem in quantum mechanics, Cambridge University Press, 1967. J. M. ZIMAN, Elements of advanced quantum theory, Cambridge University Press, 1969. A. L. FETTER, J. D. WALECKA, Quantum theory of many-particle systems, McGraw-Hill, 1971. G. E. BROWN, Many-body problems, North-Holland, 1972. G. D. MAHAN, Many-particle physics, Plenum, 1981. J. C. INKSON, Many-body theory of solids, Plenum, 1984.

424 Bibliography

B. SAKITA, Quantum theory of many-variable systems and fields, World Scientific, 1985. J. W. NEGELE, H. ORLAND, Quantum many-particle systems, Addison­Wesley, 1988. C. P. ENZ, A course on many-body theory applied to solid state physics, World Scientific, 1992.

Chapter 2

Symmetrization Principle

A. MESSIAH, Quantum mechanics, vol. II, chap. 14, North-Holland, 1976. C. COHEN-TANNOUDJI, B. DIU, F. LALOE, Quantum mechanics, vol. II, chap. 14. Wiley, 1997.

Degenerate Gases, Stability of Matter

E. LIEB, "The stability of matter", Rev. Mod. Phys., 48, 553, 1976. L. D. LANDAU, E. M. LIFCHITZ, Statistical physics, chap. 5 and 11, Perga­mon Press, 1980. J. M. LEVy-LEBLOND, F. BALIBAR, Quantique, chap. 7, Inter Editions, 1984.

Chapter 3

Second Quantization

F. A. BEREZIN, The method of second quantization, Academic Press, 1966. G. BAYM, Lectures on quantum mechanics, chap. 19, Benjamin, 1969. E. MERZBACHER, Quantum mechanics, chap. 20, Wiley, 1970. J. AVERY, Creation and annihilation operators, McGraw-Hill, 1976.

Most of the books on many-body problems and the books related to chapters 8, 9 and 10 include a presentation of second quantization.

Chapter 4

Hartree-Fock Variational Method

G. BAYM, Lectures on quantum mechanics, chap. 20, Benjamin, 1969. A. MESSIAH, Quantum mechanics, vol. II, chap. 18, North-Holland, 1976.

Bibliography 425

Electron Gas

D. PINES, P. NOZIERES, The theory of quantum liquids, Benjamin, 1966. S. RAIMES, Many-electron theory, North-Holland, 1972. M. H. MARCH, M. PARRINELLO, Collective effects in solids and liquids, chap. 2, Hilger, 1982.

The Hartree-Fock method and electron gas are covered in most of the books on many-body problems.

Chapter 5

Superconductivity Before BeS Theory

F. LONDON, Super fluids vol. I, Dover, 1960.

Bes Theory

J. BARDEEN, J. R. SCHRIEFFER, "Recent developments in superconducti­vity", in Progress in low-temperature physics III, C. J. Gorter (ed.), North­Holland, 1961. J. R. SCHRIEFFER, Theory of superconductivity, Benjamin, 1964. G. RICKAYZEN, Theory of superconductivity, Interscience, 1965. P. G. DE GENNES, Superconductivity of metals and alloys, Benjamin, 1966. R. P. FEYNMAN, Statistical mechanics, chap. 10, Benjamin, 1972. D. R. TILLEY, J. TILLEY, Super fluidity and superconductivity, Hilger, 1986. A. A. ABRIKOSOV, Fundamentals of the theory of metals, chap. 15 and 16, North-Holland, 1988.

Microscopic Interpretation of the Pseudo-Wavefunction of London

A. A. ABRIKOSOV, L. P. GORKOV, 1. E. DZYALOSHINSKI, Methods of quan­tum field theory in statistical physics, chap. 7, Prentice Hall, 1963.

Josephson Effect

P. W. ANDERSON, "The Josephson effect and quantum coherence measure­ments in superconductors and superfluids" in Progress in Low- Temperature Physics V, C. J. Gorter (ed.), North-Holland, 1967. A. A. ABRIKOSOV, Fundamentals of the theory of metals, chap. 22, North­Holland, 1988.

426 Bibliography

High-Temperature Superconductivity

"High-Temperature Superconductivity", reprints from Physical Review Let­ters and Physical Review B, January-June 1987, American Institute of Phy­sics, 1987. M. CYROT, D. PAVUNA, Introduction to superconductivity and high-Tc ma­terials, World Scientific, 1992. P. W. ANDERSON, Theory of high-temperature superconductivity in cup rates, Princeton University Press, 1997. EDS. J. BOK ET AL., The gap symmetry and fluctuations in high-Tc super­conductors NATO-ASI B371, Kluwer-Plenum, 1998.

Chapter 6

Structure of Nuclei and Nucleon Pairing

M. GOEPPERT MAYER, J. H. D. JENSEN, Elementary theory of nuclear shell structure, Wiley, 1955. A. BOHR, B. MOTTELSON, Nuclear Structure, World Scientific, 1998. A. DE SHALIT, H. FESHBACH, Theoretical nuclear physics (2 vol.), tome I: Nuclear structure, Wiley, 1974. T. MAYER-KuCKUCK, Physik der Atomkerne, Teubner, 1974. A. G. SITENKO, V. K. TARTAKOVSKY, Lectures on the theory of the nucleus, Pergamon, 1975. L. VALENTIN, Physique subatomique. Noyaux et particules, Hermann, 1975. F. IAcHELLo, A. ARIMA, The interacting boson model, Cambridge University Press, 1987. P. HUGUENIN, Theorie des paires et structure nucleaire, Lectures delivered for the 3eme cycle de la physique en Suisse Romande, 1967. R. CARSTEN, Nuclear Structure from a Simple Perspective, 2nd ed., Oxford, 2000.

Chapter 7

Superfiuidity of Liquid Helium

R. P. FEYNMAN, "Application of quantum mechanics to liquid helium" in Progress in Low Temperature Physics I, C. J. Gorter (ed.), North-Holland, 1955. K. R. ATKINS, Liquid helium, Cambridge University Press, 1959. F. LONDON, Super fluids (2 vol.), tome II, Dover, 1964. L. D. LANDAU, E. M. LIFCHlTZ, Physique statistique, chap. 6, Mir, 1967 (2nd edition).

Bibliography 427

J. WILKS, The properties of liquid and solid helium, Clarendon, 1967. R. P. FEYNMAN, Statistical mechanics, chap. 11, Benjamin, 1972. D. R. TILLEY, J. TILLEY, Super fluidity and superconductivity, Hilger, 1986. J. WILKS, D. S. BETTS, An introduction to liquid helium, Clarendon, 1987.

Chapter 8

Theory of Radiation

W. HEITLER, The quantum theory of radiation, Clarendon, 1954 (3rd edi­tion). S. M. KAY, A. MAITLAND, Quantum optics, Academic Press, 1970. R. LOUDON, The quantum theory of light, Clarendon, 1973. H. HAKEN, Light (2 vol.), North-Holland, 1981. W. P. HEALY, Non-relativistic quantum electrodynamics, Academic Press, 1982. C. COHEN-TANNOUDJI, J. DUPONT-Roc, G. GRYNBERG, Photons et atomes, Inter Editions, 1987.

General Field Theory

N. N. BOGOLIUBOV, D. V. SHIRKOV, Introduction to the theory of quantized fields, Wiley, 1959. J. D. BJORKEN, S. D. DRELL, Relativistic quantum mechanics, McGraw­Hill, 1964. J. D. BJORKEN, S. D. DRELL, Relativistic quantum fields, McGraw-Hill, 1965. P. ROMAN, Introduction to quantum field theory, Wiley, 1969. E. G. HARRIS, A pedestrian approach to quantum field theory, Wiley, 1972. V. B. BERESTETSKI, E. M. LIFCHITZ, L. P. PITAEVSKI, Relativistic quan­tum theory (2 vol.), Pergamon Press, 1977. C. ITZYKSON, J. B. ZUBER, Quantum field theory, McGraw-Hill, 1980. J. ZINN-JUSTIN, Quantum field theory and critical phenomena, Clarendon Press, 1989. M. LE BELLAC, Quantum and statistical field theory, Clarendon Press, 1991. S. WEINBERG, The quantum theory of fields (2 vol.), Cambridge University Press, 1995. M. E. PESKIN, D. V. SCHROEDER, An introduction to quantum field theory, Perseus Books. 1995.

428 Bibliography

Gauge Theories

J. LEITE LOPEZ, Gauge field theories: an introduction, Pergamon Press, 1981. E. LEADER, E. PREDAZZI, An introduction to gauge theories and the new physics, Cambridge University Press, 1982. K. MORIYASU, An elementary primer for gauge theory, World Scientific, 1983. M. GUIDRY, Gauge field theories, Wiley, 1991.

Chapter 9

Feynman Diagrams

R. A. MATTUCK, A guide to Feynman diagrams in the many-body problem, McGraw-Hill, 1967. S. M. BILENKY, Introduction to Feynman diagrams, Pergamon, 1974. M. D. SCADRON, Advanced quantum theory and its application through Feyn­man diagrams, Springer, 1979.

Most of the books on many-body problems and quantum fields present Feyn­man diagrams.

Elementary Particles, Photons and Electrons

W. E. THIRRING, Principles of quantum electrodynamics, Academic Press, 1958. R. P. FEYNMAN, Quantum electrodynamics, Benjamin, 1962. R. OMNES, Introduction to particle physics, Interscience, 1971. J. M. JAUCH, F. ROHRLICH, The theory of photons and electrons (2nd edi­tion), Springer, 1980. T. D. LEE, Particle physics and introduction to field theory, Harwood Aca­demic Publishers, 1981. T. P. CHENG, L. F. LI, Gauge theory of elementary particle physics, Cla­rendon Press, 1984. B. DE WIT, J. SMITH, Field theory in particle physics, North-Holland, 1986. B. R. MARTIN, G. SHAW, Particle physics, Wiley, 1992.

Chapter 10

Green Function Methods

A. A. ABRIKOSOV, L. P. GORKOV, 1. E. DZYALOSHINSKI, Methods of quan­tum field theory in statistical physics, Prentice Hall, 1963.

Bibliography 429

T. D. SCHULTZ, Quantum field theory and the many-body problem, Gordon and Breach, 1964. D. A. KIRZHNITS, Field theoretical methods in many-body systems, Perga­mon, 1967. E. N. ECONOMOU, Green's functions in quantum physics, Springer, 1979. G. RICKAYZEN, Green's functions and condensed matter, Academic Press, 1980.

It is suggested that the reader also refer to general books on many-body problems.

Index

Ambiguity - sign ambiguity, 177 Annihilation - operator, 93 Antimatter, 292 Antiparticle - particle-antiparticle symmetry, 291 Approximation - random phase (RPA), 150, 414

BCS theory, 159, 172 Bethe-Weizsacker - semi-empirical formula, 201 Binding - energy of the nucleus, 201 Bogoliubov - transformation, 179, 250 Bose-Einstein - and cold atoms, 70 - condensation, 69, 70, 119, 159, 227,

248,249 Boson, 61 Boundary conditions - periodic, 25, 55 Bremsstrahlung, 370

Canonical - transformation, 6, 180, 224, 250 Chain - linear harmonic chain, 42, 257 Chandrasekhar limit, 85 Charge - charge density, 148 - conjugation, 291 - density, 18, 133, 290, 313 - induced charge, 142, 148 - oscillations, 141, 147 Chronological - order, 345 Coherent - state, 9, 98, 270

Cold atoms - and Bose-Einstein condensation, 70 Compton - effect, 367, 371, 373 Condensation - Bose-Einstein condensation, 69, 70,

119, 159, 227, 248, 249 cold atoms, 70

Configuration - typical configurations, 242 Conjugation - charge conjugation, 291 Contraction, 17, 100, 181 - time-ordered contraction, 354, 356 Cooper - pair, 179, 189, 340 Coordinates - normal coordinates, 44 Coulomb - correlation energy, 140, 420 - gauge, 20, 371 - nucleo-electronic plasma, 82 Creation - operator, 92 Cross section - differential cross-section, 349 cross-section - differential cross-section, 375 Current - density, 18, 164, 169, 270, 290, 303,

313

Degeneracy - temperature of, 70 Density - charge, 148 - charge density, 18, 133, 290, 313 - current, 164, 169 - current density, 18, 270, 290, 303, 313 - energy, 18 - operator, 114

432 Index

- particle density, 103 Depth - penetration depth, 162 Diagram - Feynman diagram, 336, 361 Dielectric - function, 146, 417 Dwarf - white dwarf, 83 Dyson - equation, 388 - series, 344

Effect - Compton effect, 367, 371, 373 - isotopic effect, 172 - Meissner effect, 162, 308 - thermomechanical effect, 230 Elastic - modulus tensor, 34 Electric - field (classical), 18 - quantum electric field, 260 Electron - electron-hole pair, 76, 155, 174 - hole, 76 Emission - induced, 275 - spontaneous, 275 Energy - binding energy of the nucleus, 201 - Coulomb correlation energy, 140,

420 - density energy, 18 - Fermi energy, 76 - flux (of the field), 18 - gap, 171 - Hartree-Fock energy, 132, 137 - insertion, 385 - self-energy, 368, 385, 412, 414 - zero energy point, 261 Euler-Lagrange equations, 297 Exchange - contribution, 113 - degeneracy, 61 Exclusion - principle, 65

Fermi - energy, 76 - free Fermi field, 312 - sphere, 75 - wavenumber, 75

Fermion, 61 Ferromagnetism, 79 Feynman - diagram, 336, 361 - rules, 365, 409 Field - electric field (classical), 18 - free charged field, 289 - free Fermi field, 312 - free massive vector field, 305 - free quantum field of photons, 260 - free scalar field, 282, 372 - gauge field, 304, 310 - magnetic field (classical), 18 - quantum electric field, 260 - quantum magnetic field, 260 Fluctuations - vacuum fluctuations, 263 Flux - energy flux (of the field), 18 - quantization of flux, 170 Fluxoid, 170 Fock - space, 90 Forced - oscillator, 14, 270 Friedel - oscillations, 153 Function - dielectric function, 146, 417 - Jordan and Pauli commutation

function, 266 response function, 145

- retarded Green function, 327

Gap - energy gap, 171 Gauge - Coulomb, 21 - Coulomb gauge, 20, 21, 371 - field, 304, 310 - Lorenz gauge, 20 - principle, :304 - restricted gauge transformation, 21,

305 - transformation, 20, 301 - transformation of the first kind 107

290 ' ,

Generation - mass generation, 306 Green - one-body Green function, 393 - retarded Green function, 327

Hamiltonian - Hubbard Hamiltonian, 123 - reduced Hamiltonian, 183 Harmonic - linear harmonic chain, 42, 257 Hartree-Fock, 128 - energ~ 132, 137 Helicity, 32 Hermite - polynomials, 8 Higgs - particle, 310 - phenomenon, 306 High-Tc - superconductors, 161 Hole - electron hole, 76, 314 Hubbard Hamiltonian, 123

Insertion - energy insertion, 385 - polarization insertion, 416 - self-energy insertion, 385, 412, 414 Interaction - representation, 343 - spin-orbit interaction, 207 Isobars, 209

even-even isobars, 211 - odd isobars, 211 - odd-odd isobars, 211 Isotopic - effect, 172

Jellium, 134, 317 Jordan and Pauli - commutation function, 266

Klein-Gordon equation, 282, 305

Lame coefficients, 36 Lamb shift, 263, 380 Limit - thermodynamic limit, 55 London - equations of (superconductivity),

164 Longitudinal - component (vector field), 22, 37 Lorentz - force, 18 Lorenz - condition, 20 - gauge, 20

Index 433

Magic - doubly magic nucleus, 209 - nucleus, 209 magic numbers, 205 Magnetic - field (classical), 18 - quantum magnetic field, 260 Mass - generation, 306 - renormalization, 379 Matrix - one-body reduced density matrix,

115,395 - scattering matrix, 349 - two-body reduced density matrix,

117 Meissner - effect, 162, 308 Microcausality - principle, 267, 283

Neutron - star, 83 Normal - coordinates, 44 - product, 16, 100, 354 Nucleus - binding energy of the nucleus, 201 - doubly magic nucleus, 209 - magic nucleus, 209 Number - Fermi wavenumber, 75 - occupation number, 66 - occupation number states, 66

Observable - one-body observable, 60 - two-body observable, 60 Operator - annihilation operator, 93

creation operator, 92 - density operator, 114 - particle number operator, 91, 102,

107 - permutation operator, 60 - scattering operator, 349 Order - chronological order, 345 Oscillations - charge oscillations, 141, 147 - Friedel's oscillations, 153 Oscillator - forced oscillator, 14, 270 - harmonic oscillator, 5

434 Index

Pair - Cooper pair, 179, 189, 340 - electron-hole, 76, 155, 174 Particle - density, 103 - number operator, 91, 102, 107 - particle-antiparticle symmetry, 291 - virtual particles, 288 Penetration - depth, 162 Phonon, 41 Photon, 30, 259, 267, 270, 272, 371 - free quantum field of photons, 260 Plasma - Coulomb nucleo-electronic plasma,

82 Plasmon, 144, 148, 154 Polarization - vacuum polarization, 368, 380 - vector, 26 Polarization insertion, 416 Potential - effective potential, 143 - exchange potential, 132 - mean potential, 132 - spin-orbit potential, 208 - Yukawa potential, 285 Poynting - vector, 18, 29 Principle - exclusion principle, 65 - gauge principle, 304 - microcausality principle, 267, 283 - of symmetrization, 61 Product - normal product, 16, 100, 354 - tensor product, 58 - Wick product, 16, 101, 355 Propagator - causal propagator, 327, 356

Quantization - of flux, 170 - second quantization, 89 Quasi-particle, 41, 188

Radiative processes, 371 Radius - electromagnetic radius, 376 Random phase approximation, 150 Renormalization - mass renormalization, 379 Representation

- interaction representation, 343 Response - function, 145 RPA approximation, 150, 419

Scalar - free scalar field, 282, 372 Scattering - matrix, 349 - operator, 349 Screening, 141 - length, 143, 153 - perfect screening, 142, 143, 147, 153 Second quantization, 89 Self-energy, 368, 385, 412, 414 - insertion, 385, 412, 414 Shell, 208 Sign ambiguity, 177 Sound - second sound, 238 Space - Fock space, 90 Sphere - Fermi sphere, 75 spin-orbit - interaction, 207 - potential, 208 Squeezed - state, 50 Star - neutron star, 83 State - coherent state, 9, 98, 270 - Squeezed state, 50 - vacuum state, 90, 307 Subshell, 208 Superconductivity, 159 - London equations of, 164 Superconductors - high-Te , 161 Superfluidity, 228 Symmetrization - principle of, 61 Symmetry - particle-antiparticle symmetry, 291

Temperature - degeneracy, 70 Tensor - elastic modulus modulus, 34 - product, 58 - strain tensor, 34 - stress tensor, 34

Thermodynamic - limit, 55 Time-ordered - contraction, 354 time-ordered - contraction, 356 Transformation

Bogoliubov transformation, 179, 250 canonical transformation, 224, 250 gauge transformation, 20, 301 gauge transformation of the first kind, 107, 290

- restricted gauge transformation, 21, 305

Transverse - component (vector field), 22, 37 Two-fluid model, 233

Uncertainty relations, 8

Index 435

Vacuum - fluctuations, 263 - polarization, 368, 380 - state, 90, 307 Variational method, 127, 174 Vector - displacement vector, 34 - polarization vector, 26 - Poynting, 29 - Poynting vector, 18 Vertex, 336, 361, 373 Virtual particles, 288 Vortices, 236

Wick - product, 16, 101, 355 - theorem, 101, 180, 188, 354, 402 Wigner crystal, 135

Yukawa potential, 285

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