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Introduction to supersymmetry and supergravity. Ext. 2nd ed. (English) Zbl 0727.53077

Singapore etc.: World Scientific. xi, 425 p. £25.00/hbk; £16.00/pbk (1990).
The book is written in a pedagogical manner for beginners, complete proofs being almost always given. The material is very well exposed in 27 chapters. The introductory topic is the supersymmetry algebra. In Chapters 2-5 several approaches to the supersymmetry algebra are presented and it is shown that such an algebra should be considered as a need for both the Bose-Fermi symmetry and the principle that physics should realize the Poincaré group and an internal symmetry group in a nontrivial manner. Then, in Chapters 6 and 7 the \(N=1\) supersymmetric gauge theory and the \(N=1\) Yang-Mills theory are constructed respectively. The irreducible representations of the supersymmetry algebra are given in Chapter 8. The linearized \(N=1\) supergravity is constructed in Chapter 9 and its invariance is shown in Chapter 10. In Chapter 13 the coupling of supergravity to matter is constructed. This is done by using a local tensor calculus which is a generalization to supergravity of the rigid tensor calculus of Chapter 11. The extended rigid supersymmetry theories are presented in Chapter 12. Based on the notions of superspace and superfield of Chapter 14, in Chapters 15 and 16 the superspace formulations of the rigid supersymmetric theories and of the \(N=1\) supergravity are presented. In Chapter 17 the super-Feynman rule calculations of quantum effects in superspaces are performed and in Chapter 18 the ultraviolet properties of the extended rigid supersymmetric theories are derived. The spontaneous breaking of supersymmetry and the construction of realistic models are discussed in Chapter 19 and the supermultiplet structure to which the currents in supersymmetric theories belong is constructed in Chapter 20. Chapters 21- 24 are devoted to two-dimensional supersymmetries and contain topics as follows: two-dimensional supersymmetry algebras and their irreducible representations and rigid and local theories for supersymmetry. The superconformal groups are discussed in Chapter 25 and then the superconformal invariance is used to determine the Green functions from Chapter 26. Finally, in Chapter 27, the gauge covariant formulation of strings is presented.
In the present edition the author has added the chapters dealing with two-dimensional theories and some problems in Appendix C.
Reviewer: A.Bejancu (Iaşi)

MSC:

53C80 Applications of global differential geometry to the sciences
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83E50 Supergravity
81T60 Supersymmetric field theories in quantum mechanics
81R40 Symmetry breaking in quantum theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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