Field Theory, Quantum Gravity, And Strings Ii

Lecture Notes in Physics Edited by H. Araki, Kyoto, J.Ehlers, MLinchen,K. Hepp,ZSrich R. Kippenhahn,MSnchen,H.A. WeidenmSIler, Heidelberg J. Wess, Karlsruheand J. Zittartz, K61n Managing Editor: W. BeiglbSck 280 Field Theory, Quantum Gravity and Strings II Proceedings of a Seminar Series Held at DAPHE, Observatoire de Meudon, and LPTHE, Universit~ Pierre et Marie Curie, Paris, Between October 1985 and October 1986 Edited by H.J. de Vega and N. S&nchez Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Editors H, J. de Vega Universit~ Pierre et Marie Curie, L.P.T.H.E. Tour 16, ler 6rage, 4, place Jussieu, F-75230 Paris Cedex, France N. S~.nchez Observatoire de Paris, Section d'Astrophysique de Meudon 5, place Jules Janssen, F-92195 Meudon Principal Cedex, France ISBN 3-540-17925-9 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-17925-9 Springer-Verlag NewYork Berlin Heidelberg This work is subject to copyright. All rights are reserved,whether the whole or part of the material is concerned, specif{callythe rights of translation,reprinting, re-useof illustrations,recitation, broadcasting, reproduction on microfilmsor in other ways, and storage in data banks. Duplication of this publicationor parts thereof is only permitted under the provisionsof the German Copyright Law of .September9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violationsfall under the prosecution act of the German Copyright Law. © Springer-VerlagBerlin Heidelberg 1987 Printed in Germany Printing: Druckhaus Beltz, Hemsbach/Bergstr.; Bookbinding: J. Sch~.fferGmbH & Co. KG., GrSnstadt 215313140-543210 PREFACE This book contains the lectures delivered in the third year, Paris-Meudon 1985 - 1986, of the Seminar Series. A seminar series on current developments in mathematical physics was started in the Paris region in October 1983. The seminars are held alternately at the DAPHEObservatoire de Meudon and LPTHE-Universit& encourage theoretical physicists ticians to meet regularly. October 1983 - October Pierre et Marie Curie (Paris VI) to of different disciplines and a number of mathema- The seminars delivered in this series in the periods 1984 and October published by Springer-Verlag 1984 - October 1985 have already been as Lecture Notes in Physics, volumes 226 and 246, respectively. The present volume "Field Theory, the lectures delivered up to October Quantum Gravity and Strings, topics of current interest in field and particle theory, mechanics. Basic problems of string and superstrin~ porary perspective and quantum field theoretical cosmology are presented. cosmology and statistical theory are treated in a contem- as well as string approaches Recent progress on integrable in two, four and more dimensions II" accounts for 1986. This set of lectures contains selected is reviewed. It is a pleasure to thank all the speakers for their successful delivering comprehensive and stimulating lectures. for their interest and for their stimulating Scientific Direction "Math~matiques toire de Paris-Meudon efforts in We thank all the participants discussions. We particularly - Physique de Base" of C.N.R.S. for the financial extend our appreciation to theories and related subjects thank the and the Observa- support which made this series possible. to Springer-Verlag for thei