QUANTUM GRAVITY QUANTUM GRAVITY Edited by M. A. Markov Academy of Sciences of the USSR Moscow, USSR and P. C. West King's College London, England PLENUM PRESS • NEW YORK AND LONDON Library of Congress Cataloging in Publication Data Seminar on Quantum Gravity (2nd: 1981: Moscow, R.S.F.S.R.) Quantum gravity. "Proceedings of the Second Seminar on Quantum Gravity, held I October B-15, 1981, in Moscow, USSR"-T.p. verso. Includes bibliographical references and index. l. Quantum gravity-Congresses. 2. Cosmology-Congresses. 3. Black holes (Astronomy)-Congresses. I. Markov, M. A. (Moisei Aleksandrovich), 1908- II. West, P. C. (Peter C.) Ill. Title. QC178.S455 1981 530.1 83-24446 ISBN-13: 978-1-4612-9678-2 e-ISBN-13: 978-1-4613-2701-1 DOl: 10.1007/978-1-4613-2701-1 Proceedings of the second Seminar on Quantum Gravity, held October 13-15, 1981, in Moscow, USSR ©1984 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1984 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 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 ORGANIZING COMMITTEE Markov M.A. Chairman Frolov V.P. Scientific Secretary Zlobina K.K. Secretary Berezin V.A. Ogievetsky V.I. Tavkhelidze A.N. Fradkin E.S. EDITORIAL BOARD Markov M.A. Chief Editor Berezin V.A. Frolov V.P. PREFACE Three years have passed after the First Moscow Seminar on Quantum Gravity. It is a rather long time interval for the modern theoretical physics. The talks given at the present Second Seminar which took place in October 13-15, 1981 in Moscow contain the discussion of new results obtained during this period and the problems which arose. More than one hundred Soviet scientists and a number of the foreign guests attended this Seminar, which as the previous one was held by the Nuclear Physics Department of the Academy of Sciences of the USSR and the Institute for Nuclear Research of the Academy of Sciences of the USSR. The aim of the Seminar was to discuss the most important problems of the modern Quantum Gravity, namely: i) Quantum Gravity: the state of art; ii) Quantum effects in Cosmology; iii) Quantum black-hole physics; iv) the recent development in Supergravity and v) Quantum Gauge Theories. The Editorial Board expresses its sincere gratitude to all physicists who have contributed to these Proceedings for their cooperation with the Board in respect of time limitation, accurate and patient fulfilment of all tiresome requirements, set by the Board. The talks in the Proceedings are arranged in sections in accordance with their presentation at the Seminar. Editorial Board: M.A. Markov V.A. Berezin V.P. Frolov FOREWORD In recent years it has emerged that the nuclear weak, nuclear strong and electromagnetic forces are mediated by spin one particles whose dynamics are controlled by gauge theories within the framework of relativistic quantum field theory. Further, there is now dramatic experimental confirmation of the unification of the electromagnetic and nuclear weak forces and there exist theories which unify all of these three forces. Gravity on the other hand, the only other force of nature, is mediated by a spin two particle described by Einstein's theory of general relativity. A theme running through many articles in this book is the place of Einstein's theory in relation to the rest of physics. A major obstacle to progress in discovering the relation between the force of gravity and the other three forces of nature is the inconsistency, noticed as long ago as the 1930's, between Einstein's theory of general relativity and quantum theory as embodied in per­ turbative relativistic quantum field theory. One possible solution to this problem, which is discussed in several articles, is to modify Einstein's theory by adding terms involving higher derivatives. Al­ so discussed is the way these modifications may help alleviate one of the other problems of general relativity; namely the occurrence of singularities. Gravity is the most complex quantum field and investigation of its structure has often lead to a better understanding of quantum field theory in general. Three articles are devoted to the interplay of renormalization and symmetry within the context of gauge theories. One area where both gravity and the other forces of nature are important is in the early universe. A substantial part of the book is devoted to the processes that occur in this exotic domain. These include a discussion of how particles could have been created, in particular, the development of baryon asymmetry and how the inhomo­ genities which have led to galaxies could have emerged. One of the exciting possibilities that is considered in this context is that the universe, underwent a period of exponential expansion. It is examined to what extent this overcomes many of the problems of the standard big bang cosmology. Much work on the interplay between gravity and quantum mechanics was stimulated by the discovery that black holes can emit radiation ix x FOREWORD and matter. Eight articles are devoted to a discussion of this ef­ fect. They include the ways the laws of quantum mechanics are modi­ fied, the possibility of very small black holes, the role of thermo­ dynamics and the effect these objects could have on the evolution of the universe. Finally several authors discuss supersymmetry. This symmetry provides the only known non-trivial extension of general relativity. The extent to which these supergravity theories can provide a con­ sistent theory of gravity and quantum mechanics or may unify gravity with the three other forces of nature is examined. P.c. West CONTENTS SECTION 1. QUANTUM GRAVITY The Problems of General Relativity 1 M.A. Markov The Loss of Quantum Coherence due to Virtual Black Holes .. 19 S.W. Hawking Asymptotic Freedom in Renormalizable Gravity and Supergravity . • • . • • • . • . • . 29 E.S. Fradkin and A.A. Tseytlin Pregeometry 47 H. Terazawa On High-Frequency Background Quantization of Gravity. • . 57 H.-H. v. Borzeskowski SECTION II. QUANTUM EFFECTS IN COSMOLOGY Complete Cosmological Theories 71 L.P. Grischuk and Y.B. Zeldovich Particle Production and Dynamics in the Early Universe. • • 87 J.B. Hartle Nonsingular Model of the Universe with the Quantum­ Gravitational de Sitter Stage and its Observational Consequences •••.•••.• 103 A.A. Starobinsky Black Holes Evaporation and Big Mass Particle (Maximon, Intermediate Boson) Creation in Nonstationary Universe ..•••.••.••••.•••..•. 129 V.I. Man'ko and M.A. Markov xi xii CONTENTS Origin of the Primordial Inhomogeneities of the Universe 143 D.A. Kompaneets, V.N. Lukash and I.D. Novikov Quantum Fluctuations in Cosmology and Galaxy Formation ....... .. 161 G.V. Chibisov and V.F. Mukhanov Can de Sitter Spacetime be a Final State of the Contracting Universe? • • • • • • • • 173 V.A. Berezin A New Inflationary Universe Scenario: A possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and PrimDrdial Monopole Problems • • • 185 A.D. Linde Self-Consistent Treatment of Vacuum Quantum Effects in Isotropic Cosmology ••••••••. 197 A.A. Grib, S.G. Mamayev and V.M. Mostepanenko Quantum Field Theories with Spontaneous Symmetry Breaking in External Gravitational Fields of Cosmological Type • • • • • • . • • • • • • • 213 V.G. Lapchinsky, V.I. Nekrasov, V.A. Rubakov and A.V. Veryaskin Grand Unified Phase Transitions and the Early Universe. 231 V.A. Kuzmin, M.E. Shaposhnikov and 1.1. Tkachev SECTION III. QUANTUM EFFECTS IN BLACK HOLES On the Generalized Second-Law of Thermodynamics • • • 249 W.G. Unruh Towards the Theory of Mini Black Holes with 253 Subplanckian Mass • • • • • • • • • • Y.B. Zeldovich Spherically-Symmetric Collapse in Quantum Gravity • • • • 267 V.P. Frolov and G.A.. Vilkovisky Temperature-Dependent G and Black Hole Thermodynamics • • 291 P.C.W. Davies Vacuum Polarization Near Black Holes. • • • • • • • • • • 303 V.P. Frolov The Relativity of Vacuum • • • • • • • • • • • • • • • • 323 N. Sanchez CONTENTS xiii Black Hole Evaporations and Their Cosmological Consequences. 337 B.J. Carr SECTION IV. SUPERSYMMETRY Geometries Inherent to N = 1 Supergravity •.••• 367 A.S. Galperin, V.I. Ogievetsky and E.S. Sokatchev Currents in Supersymmetric Theories 389 P.C. West Counterterms in Extended Supergravities ••..•..•• 415 R.E. Kallosh Divergences and Anomalies in Kaluza-Klein Theories • • . 431 M.J. Duff and D.J. Toms SECTION V. GAUGE THEORIES. TWISTORS Gauge Algebra and Quantization • • 463 I.A. Batalin and G.A. Vilkovisky Renormalization of General Gauge Theories 481 I.V. Tyutin and B.L. Voronov Twistor theory 503 Z. Perjes The Group of Paths in Gravitation and Gauge Theory • • • 527 M. B. Mensky INDEX .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 547 .