Supermanifolds
2nd Edition
$84.99 (C)
Part of Cambridge Monographs on Mathematical Physics
 Author: Bryce DeWitt
 Date Published: June 1992
 availability: Available
 format: Paperback
 isbn: 9780521423779
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This is an updated and expanded second edition of a successful and wellreviewed text presenting 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. The exposition opens with the theory of analysis over supernumbers (Grassman variables), Berezin integration, supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds, with an account of superanalogs of Lie derivatives, connections, metric, 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 book then turns to applications. Chapter 5 contains an account of the Peierals bracket for superclassical dynamical systems, super Hilbert spaces, path integration for fermionic quantum systems, and simple models of Bose–Fermi supersymmetry. The sixth and final chapter, which is new in this revised edition, examines dynamical systems for which the topology of the configuration supermanifold is important. A concise but complete account is given of the pathintegral derivation of the Chern–Gauss–Bonnet formula for the Euler–Poincaré characteristic of an ordinary manifold, which is based on a simple extension of a point particle moving freely in this manifold to a supersymmetric dynamical system moving in an associated supermanifold. Many exercises are included to complement the text.
Reviews & endorsements
"...destined to become the standard work for all serious study of supersymmetric theories of physics." Nature
See more reviews"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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×Product details
 Edition: 2nd Edition
 Date Published: June 1992
 format: Paperback
 isbn: 9780521423779
 length: 428 pages
 dimensions: 229 x 152 x 24 mm
 weight: 0.63kg
 availability: Available
Table of Contents
Preface to the first edition
Preface to the second editin
1. Analysis over supernumbers
2. Supermanifolds
3. Super Lie groups: general theory
4. Super Lie groups: examples
5. Selected applications of supermanifold theory
6. Applications involving topology
References
Index.
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