Quantum Field Theory and Topology
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this bo
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Editors
M. Artin S. S. Chern 1. Coates 1. M. Frohlich H. Hironaka F. Hirzebruch L. Hormander C. C. Moore 1. K. Moser M. Nagata W. Schmidt D. S. Scott Ya. G. Sinai 1. Tits M. Waldschmidt S.Watanabe Managing Editors
M. Berger B. Eckmann S. R. S. Varadhan
Albert S. Schwarz
Quantum Field Theory and Topology With 30 Figures
Springer-Verlag Berlin Heidelberg GmbH
Albert S. Schwarz Department of Mathematics 565 Kerr Hall University of California Davis, CA 95616, USA Translators:
Eugene Yankowsky Silvio Levy Geometry Center 1300 South Second St. Minneapolis, MN 55454, USA
Title of the original Russian edition: Kvantovaya teoriya polya i topologiya. Nauka, Moscow 1989. An expanded version of the last third of the Russian edition is being published separately in English under the title: Topology for Physicists. Mathematics Subject Classification (1991): 81Txx
ISBN 978-3-642-08130-9 ISBN 978-3-662-02943-5 (eBook) DOI 10.1007/978-3-662-02943-5
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from SpringerVerlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1993 Originally published by Springer-Verlag Berlin Heidelberg New York in 1993 Softcover reprint of the hardcover 18t edition 1993 Typesetting: Camera-ready copy produced from the translation editor's output file using a Springer TEX macro package 41/3140-543210 Printed on acid-free paper
Preface
In recent years topology has firmly established itself as an important part of the physicist's mathematical toolkit. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics-suffice it to say that topological ideas play an important role in one of the suggested explanations of high-temperature superconductivity. Topology is also used in the analysis of another remarkable discovery of recent years, the quantum Hall effect. The main focus of this book is on the results of quantum field theory that are obtained by topological methods, but some topological aspects of the theory of condensed matter are also discussed. The topological concepts and theorems used in physics are very diverse, and for this reason I have included a substantial amount of purely mathematical information. This book is aimed at different classes of readers-from students who know only basic calculus, linear algebra and quantum mechanics, to specialists in quantum field theory and mathematicians who want to learn about the physical applications of topology. Part I can be considered as an introduction to quantum field theory: it discusses the b
