690 Nature Vol. 271 16 February 1978 current level of understanding of these It behoves a reviewer to draw atten­ present the material in any especially properties, calling for the most ,part on tion to faults lest it be thought that he novel or enlightening way, or to ex­ models developed to describe amor­ is a friend of the author (which he is) ploit many of the techniques of modern phous semiconductors. For liquids, of or else in league with the publishers differential geometry. H is here that course, further difficulties arise. The (which he is not). My only criticism one most feels the need for stronger local atomic configuration and hence (apart from an unfortunate interohange links with the group theory and moti­ the electronic structure changes not of the words band and bond between vating remarks. The author goes on only with time but also with tempera­ two section headings in the list of con­ to develop a detailed discussion of the ture. Thus, if measurements are made tents), is that tantalising extracts of spinor formulation of general rela­ as a function of temperature, one has theory and models, described in detail tivity, and it is particularly useful that to deal with a different material at each in later chapters, are interspersed with this approach, advocated by Roger temperature. experimental data presented earlier in Penrose, and for so long in widespread The fi eld is not short of experimental the book; yet if the reader tries the use among relativists, is dealt with in results and these are presented in theoretical chapters first, he is con­ an integrated fashion in a student text­ several chapters, one devoted to fronted with tantalising extracts of hook. It is frustrating, though, that physical ,properties, one to physico­ data. One has to learn, however, to find many useful results of spinor calculus chemical properties and metallurgical one's way around any book of this are relegated to the exercises. properties, and two others to specific kind and specialists in the field will In chapter 9, Carmeli takes up the alloys. The book is valuable for this certainly have no trouble. subject of gauge theories, and after a collection alone. It is not surprising to The price came as a pleasant sur­ preliminary discussion of electromag­ find Tl-Te alloys discussed extensively, prise (by today's standards) and the netic and Yang--Mills fields attempts since this system has not only been hook has to be good value for such an to formulate also as exhaustively investigated by the author admirable condensation of a difficult a . The Newman-Penrose himself, but also exhibits so many of subject by a leader in the field. formalism is obtained from a gauge the diverse and interesting .properties E. A. Davis theory approach, though perhaps its characteristic of liquid semiconductors. physical relevance could have been Ex.perimentalists will appreciate the E. A. Davis is Lecturer in at the better described. The Goldberg- Sachs short chapter on techniques. University of Cambridge, UK. theorem is proved in chapter 10, but its importance is not made transparent. The final two chapters of the book , however, can be fruitfully deal with solutions of the field equa­ Group theory investigated using group methods. tions of general relativity and the Especially important are those that Bondi·-Metzner- Sachs group. There or general relativity admit asymptotic symmetry groups, are also several appendices. Once again, Group Theory and General Relativity. and the formulation of concepts such all the details are competently collec­ By Moshe Carmeli. Pp. 391. (McGraw­ as asymptotic energy momentum, and ted together, but the uniotiated reader Hill: New York and Toronto, 1977.) multipole moments of the gravitational may have difficulty in understanding £16.85. field for isola·ted bodies relies heavily their wider importance or relevance. on the analysis of these groups. In Perhaps these people would do well addition to this, much attention has to consult the final paragraph of the THERE is no doubt that a textbook recently been directed to gauge Introduction which contains a quota­ which links together the topics of theories in curved , in which tion of Ahdus Salam, who learned group theory and general relativity is the gauge group continues to play an group theory from Racah: "After very welcome. The jacket of this book important part. attending these lectures I thought this proclaims that it is the first book on This book covers much of the is really too hard; I cannot learn this; " the applications of group theory to material relevant to these applications, one is hardly ever likely to need all general relativity", but l have some hut in a somewhat shapeless form. this complicated matter. I was com­ reservations about whether this is an Readers who have no previous knowl­ pletely wrong". appropriate description. Reading the edge of one or the other (or both) In spite of the specific criticisms book gives the impression of two re­ central topics may find the presenta­ concerning the presentation, I find this search monographs grafted together: tion a little stark with essential facts book a timely addition to the many one on group theory, the other general simply run off. T would recommend research papers on these two most relativity. This does not mean that the some previous background reading, at important topics. It should prove useful contents are not useful, but some least for the group theory, from the as a teaching text and, at least in con­ stronger motivation for the conjunc­ books of Naimark or Gel'fand et al. junction with some background tion of topics would have been desir­ These arc recommended by the author material, it could be used as a course able. in his introduction, and Carmeli's hook for either group theory for Field theoreticians are well used to treatment is closely similar to these. physicists, or more specifically for rela­ relying heavily on group theoretical The first six chapters contain little tivity courses. The style is straight­ techniques, particularly with the recent general relativity, dealing extensively forward and information retrieval activity in the area of gauge theories. with the representations of the rota­ easy. Many exercises are given with When it comes to general relativity, tion and Lorentz groups. Chapter 3 each chapter and an extensive biblio­ group techniques are less powerful treats the spinor representations of the graphy is added. It is elegantly pro­ because of the absence in general of Lorentz group. Chapters 4, 5 and 6 duced, and at £16.85 is not metric-preserving global diffeomor­ tackle in great depth the principal, over-expensive for a mathematical phisms. Of course, interest centres on complementary and complete series of book of this length. special model spacetimes with parti­ representations of SL(2,C). Paul Davies cular symmetries, and group theory has The author's discussion of relativity long played an elegant and useful role begins with chapter 7. The treatment Paul Davies is Lecturer in Mathematics in elucidating and classifying their is standard and traditional, and no at King's College, , properties. More general classes of attempt seems to have been made to UK.

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