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Supergravities in diverse dimensions. Commentary and reprints - in 2 volumes.(English)Zbl 0686.53061

Amsterdam etc.: North-Holland; Singapore etc.: World Scientific Publishing Ltd. (ISBN 0-444-87339-2/pbk; 0-444-87338-4/hbk; 9971-50-119-8/hbk; 9971-50-122-8/pbk). XXX, 1499 p. (1988).
The articles of this volume will not be indexed individually.
As is well known, the symmetry between bosons and fermions is called supersymmetry. The importance of this general symmetry consists in the fact that local supersymmetry must lead to supergravity.
The purpose of the present two volumes is to bring together the most important results on various supergravity theories since 1971, when the first paper on supersymmetry was written. Certainly it was a hard work for the editors to select a limited number of papers to be reproduced among the large number written over the last fifteen years. Fortunately, they succeeded in giving to the reader the right image of the evolution of research work on these fascinating topics.
The material is presented in five chapters, two are in the first volume and three in the second one. In the first chapter we find papers on classification of superalgebras and some of the original papers on supersymmetry. Chapter 2 contains papers on Poincaré and anti-de Sitter supergravity in diverse dimensions. Taking into account that eleven is the maximal dimension for which supergravity theory can exist, the editors selected papers for each dimension between eleven and one. Chapter 3 is concerned with papers on conformal supergravity theories in dimensions \(d=10,6,4,3\) and 2. This is because partial results are known in \(d=5\) and \(d=11\) and to that data no work has been done on \(d=7,8\) and 9. In Chapter 4 there are presented papers on anomalies in supergravity theories. Finally, Chapter 5 contains papers on dimensional reduction and compactification.
Each chapter contains references and useful comments of editors on the main topic treated in papers reproduced therein. We find these volumes of great importance for both physicists and mathematicians in their beautiful work on supergravity theories.
Reviewer: A.Bejancu

MSC:

53B50 Applications of local differential geometry to the sciences
53-06 Proceedings, conferences, collections, etc. pertaining to differential geometry
00Bxx Conference proceedings and collections of articles
83-06 Proceedings, conferences, collections, etc. pertaining to relativity and gravitational theory
81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory
81T60 Supersymmetric field theories in quantum mechanics
83E50 Supergravity
17A70 Superalgebras

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