Topology for Physicists
"This volume, written by someone who has made many significant contributions to mathematical physics, not least to the present dialogue between mathematicians and physicists, aims to present some of the basic material in algebraic topology at the level of
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Editors
M. Actin S.S. Chern J.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
Springer-Verlag Berlin Heidelberg GmbH
Albert S. Schwarz
Topology for Physicists With 54 Figures
Springer
Albert S. Schwarz Department of Mathematics 565 Kerr Hall University of California Davis, CA 95616, USA Translator: Silvio Levy Mathematical Sciences Research Institute 1000 Centennial Road Berkeley, CA 94720-5070, USA e-mail: [email protected] Title of the original Russian edition: Kvantovaya teoriya polya i topologiya. Nauka, Moscow 1989. This book contains an expanded version of the last third of the Russian edition. The remaining content was published in English in 1993, in the same series, under the title: Quantum Field Theory and Topology. Mathematics Subject Classification (1991): 81Txx Llb~a~y
of
Cong~ess
CatalogIng-In-PublIcatIon Data
ShvarfS. A. S. (AI bert Solo.onovlch) [Kvantova Ii teor I Ii po 1 ra I topo 1og I Ii. Eng II sh 1 Topology for physIcIsts I Albert S. Schwarz; [translator SIlvIo Levyl. -- Corrected 2nd prInt. p. CI. -- (Grundlehren der lathelatlschen Wlssenschaften ; 308) "ThIS book contaIns an expanded versIon of the last thIrd of the RussIan edItIon. The relalnlng content was publIshed In EnglIsh In 1993. In the sale serIes. under the tItle, Ouantul fIeld theory and topology"--T.p. verso. Includes bIblIographIcal references and Inde •. ISBN 978-3-642-08131-6 ISBN 978-3-662-02998-5 (eBook) DOI 10.1007/978-3-662-02998-5 1. Topology_ 2. Mathe.atlcal physIcS. I. TItle.
OC20.7.T65S4813 514--dc20
1996
II. SerIes. 96-15840 CIP
Corrected Second Printing 1996 ISSN 0072-7830 ISBN 978-3-642-08131-6 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 Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1994 Originally published by Springer-Verlag Berlin Heidelberg New York in 1994 Softcover reprint of the hardcover 1st edition 1994
Typesetting: From the translator's output file using a Springer TEX macro package SPIN 10535201 41/3143-5432 I 0 Printed on acid-free paper
Preface
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equations of motion (solitons and instantons) allow the physicist to leave the framework of
