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Les représentations linéaires du groupe de Lorentz
174
BOOK REWZWS
H E R M A N N EBERT, PhTsikalisches Ta;ehenbuch (Friedr. Viewog & 611 p. 28.80 DM)
Sohn, Braunsehw¢ig, 1962.
This is a pocket-size encyclopedia of practical physics. Long experience and painstaking weighing o f every detail have achieved this amazingly efficient condensation of useful information on almost every topic with which the physicist (the experimenter more than the theoretician) may be confronted in his daily work. The mathematical and theoretical sections are extensive and thorough, but the bulk of the book is devoted to a memorandum of basic principles and a collection of data of practical importance in all the branches of physics (including a substantial section on nuclear physics). The space allotted to each section is determined by its practical rather than its theoretical importance: thus, the nuclear physics section is essentially confined to the usual data concerning stable and radioactive isotopes, neutron cross-sections, detection and measurement of particles and radiation, but has nothing on nuclear structure: however, in this edition, a whole subsection has been added on the M6ssbauer effect. The nuclear physicist will find data o f interest throughout the whole book; e.g., scintillators are mentioned in the section on luminescence, masers in a subsection on amplifiers, formulae for energy and momentum transfer by collisions in a composite section entitled "Relativity, quantum theory". The matters are ordered according to the "decimal classification", which is one of the most dilettantish in existence. Fortunately, there is a good index. There is a very detailed and competent section (the first) on the internationally accepted systems o f units, with the appropriate symbols and conversion factors. Consistency is certainly a commendable quality, when it is exercised with moderation; the table of atomic constants would gain in utility if a practical unit o f atomic length (A or fro) had been adopted rather than the meter, and if the masses had been given in MeV rather than kgl I also take this opportunity of protesting against the intrusion of the Giorgi system (which is a practical system for electrotechnics) in theoretical electrodynamics, where it is just a nuisance. L.R. D. M. BRINK and G. R. SATCHLER, Angular momentum (Clarendon Press: Oxford University Press, London, 1962. 134 p. 15 s.) Another book on the powerful algebraic techniques developed by Wigner, Racah and their followers. It is difficult to innovate in this field; the standard treatise remains that of Fano and Racah, unequalled in systematic thoroughness and elegance. The present one, which covers the same ground, may claim, however, apart from the convenience of its pocket-size, that it is easier to read. Since, moreover, it contains all the useful tables of special formulae pertaining to the subject, it is likely to become the vade-mecum of physicists (experimenters as well as theorists) who have to deal with this algebra. L.R. M. A. NAIMARK,Les reprdsentations lindaires du groupe de Lorentz (Dunod, Paris, 1962. 384 p. 65 NF) Professor Na'imark's outstanding monograph on the representations of the Lorentz group is now available in an excellent French translation. The exhaustive treatment of the problem here presented is to a large extent the results o f work by a group of Russian mathematicians, headed by I. M. Gelfand, and to which the author belongs. He has written this book with the authority which first-hand knowledge confers, coupled with a didactic talent in the best mathematical tradition. Thanks to the skilful disposition of the argument, and the care taken by the author to define and explain all necessary concepts, the reader is not only able to find his way through the complications of the case under study, but he also learns a great deal about the use of topological and algebraic conceptions in group theory. The book is divided into four long chapters. The first two, dealing by adequate methods with the thrce-dimensional rotational group and its representations, prepare the reader for the treatment of the Lorentz group developed in the third chapter. The last chapter discusses the important question of the invariance of differential equations with respect to the Lorentz group, with some indication of its physical consequences. L.R.
BOOK REWZWS
H E R M A N N EBERT, PhTsikalisches Ta;ehenbuch (Friedr. Viewog & 611 p. 28.80 DM)
Sohn, Braunsehw¢ig, 1962.
This is a pocket-size encyclopedia of practical physics. Long experience and painstaking weighing o f every detail have achieved this amazingly efficient condensation of useful information on almost every topic with which the physicist (the experimenter more than the theoretician) may be confronted in his daily work. The mathematical and theoretical sections are extensive and thorough, but the bulk of the book is devoted to a memorandum of basic principles and a collection of data of practical importance in all the branches of physics (including a substantial section on nuclear physics). The space allotted to each section is determined by its practical rather than its theoretical importance: thus, the nuclear physics section is essentially confined to the usual data concerning stable and radioactive isotopes, neutron cross-sections, detection and measurement of particles and radiation, but has nothing on nuclear structure: however, in this edition, a whole subsection has been added on the M6ssbauer effect. The nuclear physicist will find data o f interest throughout the whole book; e.g., scintillators are mentioned in the section on luminescence, masers in a subsection on amplifiers, formulae for energy and momentum transfer by collisions in a composite section entitled "Relativity, quantum theory". The matters are ordered according to the "decimal classification", which is one of the most dilettantish in existence. Fortunately, there is a good index. There is a very detailed and competent section (the first) on the internationally accepted systems o f units, with the appropriate symbols and conversion factors. Consistency is certainly a commendable quality, when it is exercised with moderation; the table of atomic constants would gain in utility if a practical unit o f atomic length (A or fro) had been adopted rather than the meter, and if the masses had been given in MeV rather than kgl I also take this opportunity of protesting against the intrusion of the Giorgi system (which is a practical system for electrotechnics) in theoretical electrodynamics, where it is just a nuisance. L.R. D. M. BRINK and G. R. SATCHLER, Angular momentum (Clarendon Press: Oxford University Press, London, 1962. 134 p. 15 s.) Another book on the powerful algebraic techniques developed by Wigner, Racah and their followers. It is difficult to innovate in this field; the standard treatise remains that of Fano and Racah, unequalled in systematic thoroughness and elegance. The present one, which covers the same ground, may claim, however, apart from the convenience of its pocket-size, that it is easier to read. Since, moreover, it contains all the useful tables of special formulae pertaining to the subject, it is likely to become the vade-mecum of physicists (experimenters as well as theorists) who have to deal with this algebra. L.R. M. A. NAIMARK,Les reprdsentations lindaires du groupe de Lorentz (Dunod, Paris, 1962. 384 p. 65 NF) Professor Na'imark's outstanding monograph on the representations of the Lorentz group is now available in an excellent French translation. The exhaustive treatment of the problem here presented is to a large extent the results o f work by a group of Russian mathematicians, headed by I. M. Gelfand, and to which the author belongs. He has written this book with the authority which first-hand knowledge confers, coupled with a didactic talent in the best mathematical tradition. Thanks to the skilful disposition of the argument, and the care taken by the author to define and explain all necessary concepts, the reader is not only able to find his way through the complications of the case under study, but he also learns a great deal about the use of topological and algebraic conceptions in group theory. The book is divided into four long chapters. The first two, dealing by adequate methods with the thrce-dimensional rotational group and its representations, prepare the reader for the treatment of the Lorentz group developed in the third chapter. The last chapter discusses the important question of the invariance of differential equations with respect to the Lorentz group, with some indication of its physical consequences. L.R.