Recent Developments in Gravitation Cargese 1978
NATO ADVANCED STUDY INSTITUTES SERIES A series of edited volumes comprising multifaceted studies of contemporary scientific issues by some of the best scientific minds in the world, assembled in cooperation with NATO Scientific Mfairs Division. Series B: Physics RECENT VOLUMES IN THIS SERIES Volume 39 - Hadron Structure and Lepton-Hadron Interactions - Cargese 1977 edited by Maurice Levy, Jean-Louis Basdevant, David Speiser, Jacques Weyers, Raymond Gastmans, and Jean Zinn-Justin Volume 40 - Kinetics of Ion-Molecule Reactions edited by Pierre Ausloos Volume 41 - Fiber and Integrated Optics edited by D. B. Ostrowsky Volume 42 - Electrons in Disordered Metals and at Metallic Surfaces edited by P. Phariseau, B. L. Gyarffy, and L. Scheire Volume 43 - Recent Advances in Group Theory and Their Application to Spectroscopy edited by John C. Donini Volume 44 - Recent Developments in Gravitation - Cargese 1978 edited by Maurice Levy and S. Deser Volume 45 - Common Problems in Low- and Medium-Energy Nuclear Physics edited by B. Castel, B. Goulard, and F. C. Khanna Volume 46 - Nondestructive Evaluation of Semiconductor Materials and Devices edited by Jay N. Zemel Volume 47 - Site Characterization and Aggregation of Implanted Atoms in Materials edited by A. Perez and R. Coussement Volume 48 - Electron and Magnetization Densities in Molecules ana Crystals edited by P. Becker Volume 49 - New Phenomena in Lepton-Hadron Physics edited by Dietrich E. C. Fries and Julius Wess This series is published by an international board of publishers in conjunction with NATO Scientific Mfairs Division A Life Sciences B Physics C Mathematical and Physical Sciences D Behavioral and Social Sciences E Applied Sciences Plenum Publishing Corporation London and New York D. Reidel Publishing Company Dordrecht and Boston Sijthoff International Publishing Company Leiden Noordhoff International Publishing Leiden
Recent Developments in Gravitation Cargese 1978 Edited by Maurice Levy Laboratory of Theoretical Physics and High Energies Universite Pierre et Marie Curie Paris, France and S. Oeser Brandeis University Waltham, Massachusetts PLENUM PRESS. NEW YORK AND LONDON Published in cooperation with NATO Scientific Affairs Division
Library of Congress Cataloging in Publication Data Nato Advanced Study Institute on Recent Developments in Gravitation, Cargese, Corsica, 1978. Recent developments in gravitation. (NATO advanced study institutes series: Series B, Physics; v. 44) "Proceedings of the 1978 Cargese Summer Institute on Recent Developments in Gravitation, held in Cargese, Corsica, July 10-29, 1978, and sponsored in part by NATO." Includes index. 1. Gravitation -Congresses. I. Levy, Maurice 1922- II. Deser, Stanley. III. North Atlantic Treaty Organization. IV. Title. V. Series. QC178.N34 1978 531'.14 79-9174 ISBN-13:978-1-4613-2957-2 DOl: 10.1007/978-1-4613-2955-8 e-isbn-13:978-1-4613-2955-8 Proceedings of the 1978 Cargese Summer Institute on Recent Developments in Gravitation, held in Cargese, Corsica, July 10-29, 1978, and sponsored in part by NATO. 1979 Plenum Press, New York Softcover reprint of the hardcover 1st editon 1979 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher
Preface The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathematical speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications. In the last ten or fifteen years, however, the situation has changed radically. First, a great deal of significant exper~ental data became available. Then important contributions were made to the incorporation of general relativity into the framework of quantum theory. Finally, in the last three years, exciting developments took place which have placed general relativity, and all the concepts behind it, at the center of our understanding of particle physics and quantum field theory. Firstly, this is due to the fact that general relativity is really the "original non-abelian gauge theory," and that our description of quantum field interactions makes extensive use of the concept of gauge invariance. Secondly, the ideas of supersymmetry have enabled theoreticians to combine gravity with other elementary particle interactions, and to construct what is perhaps the first approach to a more finite quantum theory of gravitation, which is known as supergravity. Since many physicists are now involved in one way or another with gravitation, and since there had not been any international summer institute on the theory of gravitation for approximately ten years, it seemed to the organizers of the 1978 Cargeae Summer Institute particularly appropriate to review the whole field, starting with the classical theory of gravitation, then covering the quantum formulation, and arriving finally at the very recent developments of supergravity. A review was also included of the present exper~ental status of the theory of gravitation. Thus, the 1978 Swnmer Institute brought together the "classical" specialists of general relativity who were interested in learning more about recent developments and the elementary particle physicists who wanted to familiarize themselves with the mathematical and experimental framework of gravitation. It was, in all v
vi PREFACE respects, very successful, showing the validity of the original idea. Thanks to the active cooperation of all the lecturers we were able to bring quickly together the texts of all the courses given at Cargese. This enables us to present here a relatively complete review of many aspects of the theory of gravitation. This book should be extremely useful therefore to all the physicists who want to learn about recent developments, or to the specialists in other branches of physics who want to incorporate general relativity into their work. This Summer Institute was made possible by a grant from the Scientific Committee of NATO, within its Advanced Study Institutes Programme. It is a pleasure to thank its members for their encouragement and understanding. We would also like to thank three organizations in France which helped us financially: the D~legation Generale; la Recherche Scientifique et Technique (DGRST), the Centre National de la Recherche Scientifique (CNRS) and the Institute National d'astronomie et de Geophysique (INAG). Our thanks are also due to the National Science Foundation in the United States, to' the University of Nice and to the "Universite Pierre et Marie Curie" in Paris, who all helped in one way or another. Finally, we would like to thank all those who worked very hard to organize the Institute, particularly Dr. Jean-Louis BaHdevant and Miss Marie-France Hanseler, and of course, all the lecturers, without whose efforts and enthusiasm nothing would have been possible. Maurice Levy Stanley Deser
CONTENTS PART I: CLASSICAL RELATIVITY The Status of Experimental Gravitation B. Bertotti An Introduction to General Relativity and Its Recent Achievements Y. Choquet-Bruhat Underlying Mathematical Structures of Classical Gravitation Theory B. Carter 3 23 41 PART II: QUANTUM GRAVITY Euclidean Quantum Gravity S. W. Hawking Quantum Field Theory Renormalization in Curved Space-Time D. G. Boulware Aspects of Quantum Field Theory in Curved Space-Time: Effective Action and Energy-Momentum Tensor L. Parker 145 175 219 The Formal Structure of Quantum Gravity 275 B. S. De Witt Quantum Gravity: A Fundamental Problem and Some Radical Ideas G. 't Hooft 323 vii
viii Quantum Field Theory and Fibre Bundles in General Space-Time S. J. Avis and C. J. Isham CONTENTS 347 PART III: SUPERGRAVITY Supergravity and Superspace B. Zumino The Dynamics of Supergravity S. Deser Extended Super symmetry and Extended Supergravity Theories J. Scherk 405 461 479 Lectures in Supergravity Theory 519 P. Van Nieuwenhuizen Irreducible Representations of Supersymmetry (Seminar) D. Z. Freedman Massive Gravitinos (Seminar) S. Ferrara Anomalies in Supersymmetric Theories (Seminar) M. T. Grisaru Index 549 563 577 593