Modern Group Theoretical Methods in Physics: Proceedings of the Conference in Honour of Guy Rideau

329 Pages·1995·12.638 MB·English

by  Robert L. Anderson, Nail H. Ibragimov (auth.), J. Bertrand, M. Flato, J.-P. Gazeau, M. Irac-Astaud, D. Sternheimer (eds.)

Modem Group Theoretical Methods in Physics
MAT HEMA TICAL PHYSICS STUDIES
Series Editor:
M. FLATO, Universite de Bourgogne, Dijon, France
VOLUME 18
Modem Group Theoretical Methods
in Physics
Proceedings of the Conference
in Honour of Guy Rideau
edited by
J. Bertrand
L.P.T.M.,
Universite Denis Diderot,
Paris, France
M. Flato
Universite de Bourgogne,
Dijon, France
J.-P. Gazeau
M. Irac-Astaud
and
D. Stemheimer
L.P.T.M.,
Universite Denis Diderot,
Paris, France
Springer-Science+Business Media, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
Printed on acid-free paper
All Rights Reserved
ISBN 978-90-481-4598-0 ISBN 978-94-015-8543-9 (eBook)
DOI 10.1007/978-94-015-8543-9
© 1995 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1995.
Softcover reprint of the hardcover 1s t edition 1995
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.
To our friend Guy Rideau upon his retirement from CNRS
Table of Contents
Opening Address
Moshe Flato Xl
The publications of Guy Rideau
XV
The Problem of Invariants for Lie-Bäcklund Groups
Robert L. Anderson and Nail H. Ibragimov 1
Galilean Coherent States and Wavelets
J.-P. Antoine 15
On the U se of Quantum Algebras in Rotation-Vibration Spectros
copy
R. Barbier and M. Kibler 27
Invariant Differential Calculus on aDeformation ofthe Weyl
Heisenberg Algebra
J. Bertrand and M. Irac-Astaud 37
Noncompact Topological Quantum Groups
F. Bidegain 51
Symmetric Symplectic Manifolds and Deformation Quantization
P. Bieliavsky, M. Cahen and S. Gutt 63
The Conformal Invariance of the Klein-Gordon Equation in 1+ 1
Dimension
S. de Bievre and J. Renaud 75
Compact Topological Quantum Groups
P. Bonneau 87
Groupes de Transformations des Varietes Statistiques
G. Burdet andl M. Perrin 97
viii
Non-Frustrated Signed Graphs
Ph. Combe and H. Nencka 105
De I 'Ubiquite de la Condition KMS
G.G.Emch 115
A Model for QCD in Three Dimensions
C. Fnmsdal 129
Poisson Path Integral Representation of Green Functions for
Certain Field Theories
B. Gaveau, 1. Bertrand and G. Rideau 143
Diffeomorphism Group Representations and Nonlinear Quantum
Theories
G.G. Goldin 157
Conditional Symmetries for 1s t order Systems of PDES in the
Context of the Clairin Method
A.M. Grundland and G. Rideau 167
Quasistationary Approximation and Gauge Invariance in Classical
Electrodynamics
A. Heslot 179
Graded Poisson Brackets and Field Theory
Y. Kosmann-Schwarzbach 189
The Basic Lemma in the Theory of Formal Groups
C. Moreno and F. Galvez 197
Spectra and Generalized Eigenfunctions of the One- and Two
Mode Squeezing Operators in Quantum Optics
B. Nagel 211
A Higgs-free Model for Fundamental Interactions
M. Pawlowski and R. [email protected] 221
Coupled Hodgkin Huxley Neurons with Stochastic Synaptic Inputs
R. Rodriguez 233
ix
Initial Data for Non-Linear Evolution Equations and Differentiable
Vectors of Group Representations
J.C.H. Simon and E. Taflin 243
Star Products: Their Ubiquity and Unicity
D. Sternheimer 255
Finite Braid Groups for the SU(2) Knizhnik Zamolodchikov
Equation
LT. Todorov 267
Continuous Symmetries of Differential-Difference Equations
P. Wintemitz and D. Levi 271
Processus Limites et Irreversibilite en Mecanique Statistique hors
d 'Equilibre
Raymond Jancel 283
Allocution de Clöture
Guy Rideau 315
GUY RIDEAU