Geometric Methods in Mathematical Physics Proceedings of an NSF-CBMS
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Geometric Methods in Mathematical Physics Proceedings of an NSF-CBMS Conference Held at the University of Lowell, Massachusetts, March 19-23, 1979
Edited by G. Kaiser and J. E. Marsden
Springer-Verlag Berlin Heidelberg New York 1980
Editors Gerald Kaiser Mathematics Department University of Lowell Lowell, M A 01854 USA Jerrold E. Marsden Department of Mathematics University of California Berkeley, C A 9 4 7 2 0 USA
A M S Subject Classifications (1980): 5 3 C X X , 5 8 F X X , 7 3 C 5 0 , 81-XX, 83CXX ISBN 3-540-09742-2 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-38?-09742-2 Springer-Verlag NewYork Heidelberg Berlin Library of Congress Cataloging in Publication Data. Main entry under title: Geometric methods in mathematical physics. (Lecture notes in mathematics; 775) Includes bibliographies and index. 1. Geometry, Differential--Congresses.2. Mathematical physics--Congresses.I. Kaiser, Gerald. I1.Marsden, Jerrold E. III. United States. National Science Foundation.IV. Conference Board of the MathematicalSciences. V. Series: Lecture notes in mathematics (Berlin); 7"75. QA3.L28 no. ?75 [QC20.7.G44] 510s 80-332 ISBN 0-387-09742-2 [5t6.3'6] 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-Verlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
Introduction This volume represents invited papers presented at the CBMS regional conference held at the University of Lowell~ March 19-23.
The theme of the con-
ference was geometric methods in mathematical physics and the papers were chosen with this in mind. It is really only in the last couple of decades that the usefulness of geometric methods in mathematical physics has been brought to light.
In other
branches of mathematics their usefulness has been clearly demonstrated by Riemann, Poincare and Cartan; a modern example is the use of symp!ectic geometry in group representations by Kirillov and Kostant.
Save for general relativity~ mathematical
physics has been dominated primarily by analytical techniques.
The excitement
of
the past few decades has been the complementing power of geometric methods. The proper geometrization of classical mechanics started with Poincare and continued with many workers, Sci.
(1948)).
such as Synge (Phil. Trans.
(1926)) and Reeb (C. R. Acad.
However, it wasn't until the analysis led to and became inextricably
involved with geometry through the deep works of Kolmogorov, Arnold and Moser in celestical mechanics that a permanent bond became reality.
The success of
symplectic geometry in classical mechanics has mot
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