I 10.D [ Nuclear Physics A90 (1967) 705--707; (~) North-Holland Publishing Co., Amsterdam

BOOK REVIEWS

G. HEBER, Mathematische Hilfsmittel der Physik I (Akademie-Verlag, Berlin, 1966. 162 p. 8 M D N )

A very handy pocket-size repertory o f the main mathemat ica l definitions, me thods and formulae currently used by the physicists. This first booklet conta ins calculus, vectors and tensors, series (in- c luding expansions in te rms of o r thonorma l systems) , error statistics, matr ices and operators , func- t ions o f a complex variable. A l though the systematic a r r angemen t makes it easy to find any needed piece o f informat ion, an alphabetical index affords the user fur ther help in this respect. This par t icular repertory, wisely limited to essentials, seems to me the best conceived and most practical of those 1 have seen.

L.R.

m,. STEHLr, Quantum mechanics (Holden-Day, San Francisco, 1966, ~iii-263 p. $10.75)

With its decidedly practical or ientat ion, this text is well-suited to give s tudents a sound working knowledge o f non-relativistic q u a n t u m mechanics ,

L.R.

Analytical Chemist ry , Progress in Nuclear Energy, series IX, Vol. 4 (Pergamon Press, 1966. 166 p.)

It is difficult for publishers to keep up with progress in nuclear energy; m o n o g r a p h s tend to be obsolete even before they are printed. This is also true o f the present volume, which conta ins four articles: Niels J. Hansen , Solid State Charged Particle Detectors; Vincent P. Guinn , Advances in Neu t ron Activat ion Analysis; I). L ich tman and R. B. McQuis tan , Slow Electron Interaction with Adsorbed Gases; J. E. Strain, Use o f Neu t ron Genera tors in Activat ion Analysis .

These articles are well writ ten and give a good account o f the state of their subjects - at the t ime of writing. Only Gu inn gives informat ion on this point; his contr ibut ion was presented at the Geneva Conference in 1964 and was publ ished in the proceedings, which appeared last year. Hansen ' s article is probably even older, whereas the remain ing two papers are slightly more recent.

Much progress has taken place in these fields in the last two years, and the analytical chemist who migh t wish to bring his knowledge up to date will find no informat ion on the use o f l i thium drifted ge rman ium detectors, sealed tube neut ron generators and many other recent addi t ions to the nuclear analytical capacity.

K. Heydorn

A. A. ABRIKOSOV, L. P. GOR'KOV and 1. YE. OZYALOSHINSKII, Quantum field theoretical methods in statistiealphysics (Pergamon Press, Oxford, 1965. xii-365 p. 70s).

This is an impor tan t book; it conta ins a t ho rough and author i ta t ive account o f the new m e t h o d s in t roduced in the s tudy of sys tems of particles in s t rong interaction, and of the principal appl icat ions i l lustrat ing the wide scope and power o f these methods . The title (alledgedly English) in tends to indicate that the me thods in quest ion have first been developed in the q u a n t u m theory o f fields; how- ever, this is jus t a historical accident, for the abst ract s t ructure o f the mathemat ica l a lgorisms in quest ion is so general tha t they can be applied to a wide range of physical s i tuat ions, otherwise un- related. The case is ana logous to tha t o f the theory o f groups, and it would be better to designate these me thods by their mathemat ica l names than by reference to one o f their doma ins of application. The first me thod is - rather trivially - based on the use o f creation and annihi la t ion operators , act ing on state vectors characterized by number s o f occupat ion o f individual states; what confers this formal descript ion its real impor tance is the addi t ion o f a dynamical element, the concept of "quasi -par t ic le" . The other, still more powerful, me thod consists in the systematic use o f Green functions, or propaga-

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tors, to express the effect o f the interactions between pairs o f elements o f the system; this mus t be coupled with some general procedure for the exhaust ive enumera t ion o f all types o f interacting pairs, - a topological problem conveniently formulated in graphical form. On this basis, it has been possible not only to obtain a qualitative unders tanding, but to a large extent to perform a quant i ta t ive anal- ysis o f such remarkable p h e n o m e n a as superconduct ivi ty and superfluidity. For the reason indicated above, the same methods have also found fruitful applicat ion in the theory o f nuclear structure, where they have led to explanat ion o f the " g a p " in the energy spec t rum o f e v e n nuclei and have made possible a detailed analysis o f the collective excitations o f the nuclear const i tuents . The book under review is mainly concerned with a systematic exposit ion o f the application o f the new me thods to general sys tems of fermions and bosons. It also gives a concise and lucid account of the main features o f superfluidity and a more lengthy discussion o f superconduct ivi ty; there is also a chapter on long- wave electromagnetic radiat ion in dense media. The t rea tment natural ly makes extensive use o f the brilliant contr ibut ions made by the Russian school under Landau ' s leadership, but it does full justice to the no less fundamenta l work o f other physicists, f rom which Landau himself derived much in- spiration. (I know, for instance, from a conversat ion at the Kiev conference, Landau ' s warm ad- mirat ion for the work o f Matsubara . ) The present English t ranslat ion is brought up- to-date by sub- stantial addi t ions supplied by the authors ; hence its designation as a "second edit ion". The print ing and product ion are o f the highest quality.

L.R.

M. TXNKHAM, Superconductiz,ity (Gordon and Breach, New York, 1965. 84 p. paper $2.50, bound $4.50)

P. G. Dt! GrNtqrs, Superconductirity of metals and alloys (Benjamin, New York, 1966. xiv-274 p. Cloth S12.50)

These two monographs are complementa ry in the sense that the reader o f the latter is referred to the former for a more tho rough theoretical discussion o f the foundat ions . Taken together, they pro- vide a competent and up-to-date survey o f the whole subject.

L.R.

M. GOURDIN, Diffusion des dlectrons de haute dnergie (Masson, Paris, 1966. 229 p.)

Bonne monographie , quoique parfois un peu sommaire , et ma lheureusemen t ddparde par un abus , frisant le scandale, d 'am6ricanismes abso lumen t superflus. 11 est regrettable dgalement que la typo- graphie, dans la composi t ion des formules, s 'dcarte des rhgles usuelles, au grand ddpends de la Idgi- bilitd. Les bonnes r~gles, d 'ail leurs tr4s simples, sont dnoncdes dans les r ecommanda t ions de la Com- miss ions des Symboles, Unitds et Nomenc la tu re de I ' IUPAP.

L.R.

K. GOTTFRIED, Quantum mechanics, Vol. i: Fundamen ta l s (Benjamin, New York, 1966. xvii-494 p.)

A textbook in the highest class. The author , with becoming modesty, tells us that he is heavily in Dirac 's and Pauli 's debt. Who is not? Students will henceforth be indebted to him for being int roduced in such a master ly fashion to the great masters ' original concept ions as well as to the latest ref inements they have received. The delight which also seasoned physicists will find in a perusal o f the book is enhanced by a remarkably fine typographical set-up, which does honou r to the enterprising publisher. (The only formal blemish is the use o f aberrant unit symbols , such as ev instead of eV, which ought no longer to be tolerated, especially not in a textbook.)

I should have liked to s top here, but 1 mus t end, regretfully, on a " tu quoque"! . The au thor ' s pil- gr image to Copenhagen has apparent ly not made him qui te firm enough to wi ths tand the subtle pr incetonian heresies, which he quotes approvingly in a footnote on p. 788. Let us hope that this footnote, which spoils an otherwise excellent discussion o f the epistemological quest ions, will be turned into its negat ion in the next edition.

L.R.