mathematische hilfsmittel der physik i: g. heber, (akademie-verlag, berlin, 1966. 162 p. 8 mdn)

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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