Differential Geometrical Methods in Mathematical Physics II Proceedi
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676 Differential Geometrical Methods in Mathematical Physics II Proceedings, University of Bonn, July 13-16,1977
Edited by K. Bleuler, H. R. Petry and A. Reetz
Springer-Verlag Berlin Heidelberg New York 1978
Editors: Konrad Bleuler Axel Reetz Herbert Rainer Petry Institut fUr theoretische Kernphysik der Universitat Bonn Nussallee 14-16 0-5300 Bonn
Library of Congress Cataloging in Publication Data
Main entry under title:
Differential geometrical methods in mathematical physics. (Lecture notes in mathematics 676) Bibliography: p. Includes index. 1. Geometry, Differential--Congresses. 2. Mathematical physics--Congresses. I. Bleuler, Konrad, 1912II. Reetz, Axel, 1937III. Series: Lecture notes in mathematics (Berlin) ; 676. QA3.L28 no. 676 [QC20.7.D52] 510'.8s [530.1'5'636] 78-12108 AMS Subject Classifications (1970): 17A30, 53AXX,53BXX, 53CXX, 53C50, 55BXX, 55FXX, 55F25, 57015, 57020, 57030, 58AlO, 58F05, 70 H15, 81-02, 83CXX
ISBN 3-540-08935-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08935-7 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Veriag Serlin Heidelberg 1978
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PRE F ACE Applications of modern differential geometry to theoretical physics became of greatest importance during recent years. In particular, the new gauge theories, which yield the fundamental coupling schemes between elementary particles, exhibit most interesting geometrical and topological aspects. Differential geometry plays, however, also an important role in various other branches of physics: a characteristic example constitutes geometric quantization which is not only of basic physical interest but became, at the same time, a fruitful field of pure mathematical research. In addition, geometrical viewpoints remain decisive tools in our understanding of Einstein's theory of gravitation, both in its classical form and in the more recent developments connected with the transition to quantum theory. These three topics were discussed during the last Bonn conference, and the various contributions are collected in the three corresponding chapters of this volume (comp. the index overleaf). In addition, there is an introductory chapter by S. Sternberg in which the basic geometrical structures of physical field theories are worked out explicitely. Chapter I on gauge theories starts with a lecture of M.E. Mayer who emphasizes the role of characteristic classes in the classification of the underlying principal bundles of the physical gauge fields. The contributions of M. Carmeli
