Quantum Gravity

543 Pages·1984·21.56 MB·English

by  M. A. Markov (auth.), M. A. Markov, P. C. West (eds.)

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,
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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