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Supermanifolds (Cambridge Monographs on Mathematical Physics),Used
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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 BoseFermi 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 ChernGaussBonnet formula for the EulerPoincar 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.
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- Q: What is the primary focus of 'Supermanifolds' by Bryce DeWitt? A: The book primarily focuses on the modern theory of supermanifolds, providing a detailed exposition that includes analysis over supernumbers, Berezin integration, and the super-analogs of ordinary manifold theory.
- Q: Is this book suitable for beginners in mathematics? A: While the book is comprehensive, it is recommended for readers who have a foundational understanding of advanced mathematics, particularly in the areas of manifold theory and algebra.
- Q: What topics are covered in the second edition of 'Supermanifolds'? A: The second edition covers supervector spaces, super Lie groups, applications in quantum systems, and includes a new chapter on dynamical systems related to the configuration supermanifold.
- Q: Does the book include exercises for practice? A: Yes, 'Supermanifolds' includes many exercises designed to complement the text and enhance understanding of the material.
- Q: What is the publication date of this edition? A: The second edition of 'Supermanifolds' was published on May 28, 1992.
- Q: What is the item condition of this book? A: The item is listed as 'New', ensuring that it is in excellent condition for readers.
- Q: How many pages does 'Supermanifolds' contain? A: The book contains a total of 432 pages.
- Q: What type of binding does this book have? A: The book is available in a paperback binding.
- Q: Who is the author of 'Supermanifolds'? A: The author of 'Supermanifolds' is Bryce DeWitt.
- Q: What is the significance of the Chern–Gauss–Bonnet formula discussed in the book? A: The book provides a path-integral derivation of the Chern–Gauss–Bonnet formula, which relates the topology of a manifold to its geometry, an important concept in differential geometry.