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This book presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory. The exposition opens with the theory of analysis over supernumbers (Grassmann variables), Berezin integration, supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds, with an account of the super-analog of Lie derivatives, connections, metrics, curvature, geodesics, Killing flows, conformal groups, etc. The book goes on to discuss the theory of super Lie groups, super Lie algebras, and invariant geometrical structures on coset spaces. Complete descriptions are given of all the simple super Lie groups. The final chapter contains an account of the Peierls bracket for superclassical dynamical systems, super Hilbert spaces, path integration for fermionic quantum systems, and simple models of Bose-Fermi supersymmetry. Many exercises are included to supplement the material in the text.
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This updated and expanded second edition of an established text presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the superanalogs of all the basic structures of ordinary manifold theory.Review:
"...destined to become the standard work for all serious study of super-symmetric theories of physics." Nature
"The material is not presented in the manifestly rigorous style of modern mathematics, but in a style which in my opinion is entirely appropriate for the presentation of serious new mathematics to theoretical physicists; explanations are always admirably lucid, and the motivation for each step is clearly described. Alice Rogers, Mathematical Reviews
"I recommend the book to those hardy souls who wish to venture out into the stormy waters of current particle theory." Arthur S. Wightman, Physics Today
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Book Description Cambridge University Press, 1986. Condition: New. book. Seller Inventory # M0521311764