Table Of ContentFIELD THEORY, QUANTIZATION AND STATISTICAL PHYSICS
MATHEMATICAL PHYSICS AND
APPLIED MATHEMATICS
Editors:
M. FLA TO, Universite de Dijon, Dijon, France
R. R.-\CZKA, Institute of Nuclear Research, Warsaw, Poland
with the collaboration of:
M. GUENIN, Institut de Physique Theorique, Geneva, Switzerland
D. STERNHEIMER, College de France, Paris, France
VOLUME 6
FIELD THEORY,
QUANTIZATION AND
STATISTICAL PHYSICS
In Memory of Bernard Jouvet
Edited by
E. TIRAPEGUI
D. REIDEL PUBLISHING COMPANY
DORDRECHT :HOLLAND / BOSTON :U.S.A.
LONDON :ENGLAND
Library of Congress Cataloging in Publication Data
Main entry under title:
Field theory, quantization, and statistical physics.
(Mathematical physics and applied mathematics; v. 6)
Includes bibliographical references and index.
I. Quantum field theory-Addresses, essays, lectures.
2. Statistical physics-Addresses, essays, lectures. 3. Jouvet, Bernard,
1927-1978. I. Tirapegui, E., 1940- II. Jouvet, Bernard, 1927-
1978. III. Series.
QCI74.46.F53 530.1' 43 80-24425
ISBN-13: 978-94-009-8370-0 e-ISBN-13: 978-94-009-8368-7
DOl: 10.1007/978-94-009-8368-7
Published by D. Reidel Publishing Company,
P.O. Box 17,3300 AA Dordrecht, Holland
Sold and distributed in the U.S.A. and Canada
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In all other countries, sold and distributed
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D. Reidel Publishing Company is a member of the Kluwer Group
All Rights Reserved
Copyright © 1981 by D. Reidel Publishing Company, Dordreclit, Holland.
Softcover reprint of the hardcover I 5t edition 1981
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
BERNARD JOUVET (1927-1978)
FOREWORD
It is with great emotion that we present here this volume dedicated to the
memory of Bernard Jouvet, Docteur es Sciences, Directeur des Recher-
ches at the Centre National pour la Recherche Scientifique.
The life and the career as a physicist of Professor Jouvet are evoked in
the following pages by Professor F. Cerulus, a friend of long standing of
Professor Jouvet. The contributions have been written by physicists who
were friends, collaborators or former students of Professor Jouvet.
I express here my gratitude for their contributions.
I wish also to thank Mrs. France Jouvet for her kind help in the realiza-
tion of this book. Without her support this would have been impossible.
I am also especially indebted to Professor M. Flato for his constant
encouragement and kind cooperation, and to F. Langouche and D.
Roekaerts for their generous help in the preparation of this volume.
E. TIRAPEGUI
TABLE OF CONTENTS
FOREWORD VII
BIOGRAPHICAL SKETCH XI
LIST OF SELECTED SCIENTIFIC PUBLICA TIONS XIX
PART ONE: FIELD THEORY AND QUANTIZATION
C. BECCHI, A. ROUET and R. sToRA/Renormalizable Theories
with Symmetry Breaking 3
J. CALMET and A. VISCONTI/Computing Methods in Quantum
Electrodynamics 33
GERARD CLEMENT/Classical Mechanics of Autocomposite
Particles 59
s. DEsER/Exclusion of Static Solutions in Gravity-Matter
Coupling 77
D. ARNAL, J. C. COR TET, M. FLATO and D. STERNHEIMER/
Star-Products: Quantization and Representations without
Operators 85
R. GASTMANs/High Energy Tests of Quantum Electrodynamics 113
L. GOMBEROFF and E. K. MASCHKE/Non-Ideal Effects on the
Stability of a Cylindrical Current-Carrying Plasma 123
LEOPOLD HALPERN/Broken Symmetry of Lie Groups of Trans-
formation Generating General Relativistic Theories of
Gravitation 147
J. c. HOU ARD and M. IRAC-AST AUD/Ward-Takahashi Identities
and Gauge Invariance 161
A. PE'fERMAN/Towards the Early Stages of the Universe 183
G. RIDEAu/Covariant Quantizations of the Maxwell Field 201
F. STRoccHI/Gauss' Law in Local Quantum Field Theory 227
E. c. G. SUDARSHAN/Discrete States Buried in the Continuum 237
x T ABLE OF CONTENTS
PART TWO: STATISTICAL PHYSICS
P. COULLET and c. TRESsER/Some Universal Aspects of the
Transition to Stochasticity for Non-Conservative Dynamical
Systems 249
CHARLES P. ENz/Hydrodynamic Models with Random Forces 263
ARNO HOLZ/High-Temperature Study of Planar Rotator- and
XY-Models for Dimensions D ~ 2 277
F. LANGOUCHE, D. ROEKAERTS and E. TIRAPEGUI/General
Langevin Equations and Functional Integration 295
INDEX 319
BIOGRAPHICAL SKETCH
Bernard Pierre Fran<;ois Jouvet was born on February 5th, 1927, in
Lons-le-Saunier, a small provincial town in the Jura hills in the eastern
part of France, near the Swiss border. His father, Andre Jouvet, was a
physician and Bernard was the youngest child of three sons and one
daughter.
He went to school in his home town and obtained the 'baccalaureat'
in 1945. The next two years were spent at the Lycee du Parc in Lyon
studying mathematics (,Math. Elem.' and 'Math. Sup.') in preparation
for his university studies. These took place in Paris and he obtained his
first degree, the 'licence es science', in 1949. He married in the same year.
He had known his fiancee, France Tournier, for many years, already at
the Lycee in Lons-Ie-Saunier; she was to give him a lifelong happy home
and three sons.
In 1950 he obtained a fellowship of the Centre National pour la
Recherche Scientifique (CNRS), the official French research organisation.
He felt inclined to theoretical research and had been noticed by his
professors, especially by A. Proca whose research group he joined at the
Institut Henri Poincare.
Amidst this group and at the Proca seminar he learned of Feynman's
methods and of the decisive progress which had been made in quantized
field theory. Almost all of these discoveries had been made in the U.S.A.
during the years 1945-1949 and, because of the war and its aftermath,
their development had taken place without any participation by French
physicists. Most of the new methods were discovered by fairly young men
in research groups with which - even before the 1939-1945 war - the
French theorists had few - if any - personal contacts.
The efforts of Jouvet and his fellow-students at the Institut Henri
Poincare were, therefore, exclusively directed towards understanding the
printed publications without the benefit of a verbal and intuitive initiation
into this new field of theoretical physics but also without the concomitant
prejudices. In addition to this were the cramped quarters at the Institut
Henri Poincare and the habits of its members which resulted in Jouvet
working mostly at home. As a new idea came to his mind he would
Xl
XII BIOGRAPHICAL SKETCH
examine and develop it by himself and discuss it in the group when it was
already fairly well thought-out.
At the beginning of his research activity in 1949 Proca suggested that he
should look at the symmetry between space and time which Schwinger
had managed to build into his theory of relativistic quantum fields.
Jouvet was therefore induced to study seriously relativity theory and its
supporting mathematics. He noticed a puzzling analogy between the
mechanical equation of motion and Maxwell's equation of the electro-
magnetic field. By a formal treatment, copying the methods of special
relativity, he proposed an extension of the electromagnetic theory;
this meant that, for constant fields at least, the contraction of the electro-
magnetic tensor (F!,v F!'V) would be bounded by a constant. He then
envisaged a further extension, analogous to the transition from special
to general relativity, to Riemannian space for non-constant fields with the
hope that this could perhaps provide a cure for the divergence of the
electron self energy; this meant, however, a non-linear theory. Proca
suggested at this point a comparison with the non-linear electrodynamics
of M. Born, and J ouvet followed the hint. His expose of the Born theory
and of his own theory was presented as the required thesis for the degree
'diplome d'etudes superieures' in 1950. In 1951 he obtained a position of
research fellow (,attache de recherche') at the CNRS and spent two months
at the summer school of theoretical physics at Les Houches.
Proca arranged for Jouvet to present his theory to W. Pauli when the
latter came to Paris that same year. Pauli was apparently favourably
impressed for he invited Jouvet to come to Zurich for three months in the
spring of 1952.
A few days after his arrival in Zurich Jouvet explained his work in
detail to Pauli and Schafroth; the next day Pauli proved that the envisaged
generalization could not work and proposed that Jouvet should turn his
attention to nuclear physics and try to find the magic numbers in the
shell model by using a Thomas- Fermi method for the nucleus.
Jouvet thought the problem over and came up with a novel way of
computing by introducing a variational method. Numerically it was very
succesful and predicted the spins of quite a few nuclei, some of which
were known at the time and others were subsequently verified. He
realised, too, that the success of the method depended crucially on an
invariance property of his trial wave functions for which he had no physi-
cal justification. Pauli appreciated the swiftness Jouvet had demonstrated
in this research and the lucid analysis in presenting it, and he invited him
for another three months the following spring.
