Table Of ContentMathematical Physics
and
Stochastic Analysis
Essays in Honour of Ludwig Streit
This page is intentionally left blank
Mathematical Physics
and
Stochastic Analysis
Essays in Honour of Ludwig Streit
Editors
S. Albeverio, Ph. Blanchard, L Ferreira,
T. Hida, Y. Kondratiev and R. Vilela Mendes
ttf>e World Scientific
Singapore • New Jersey • London • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P O Box 128. Farrer Road. Singapore 912805
USA office: Suite IB. 1060 Main Street, River Edge. NJ 07661
UK office: 57 Shelton Street. Covent Garden. London WC2H 9HE
British Library Cataloguing-in-Publlcation Data
A catalogue record for this book is available from the British Library.
MATHEMATICAL PHYSICS AND STOCHASTIC ANALYSIS:
Essays In Honour of Ludwlg Streit
Copyright ® 2000 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means.
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center. Inc.. 222 Rosewood Drive. Danvers, MA 01923. USA. In this case permission to
photocopy is not required from the publisher.
ISBN 981-02-4440-1
Printed in Singapore by World Scientific Printers
V
Preface
In October 1998 a conference took place in Lisbon to celebrate Ludwig's
Streit 60th birthday. This book assembles some of the papers presented at
the conference as well as other essays contributed by the many friends and
collaborators that wanted to honor Ludwig Streit's scientific career and
personality.
Ludwig Streit was born June 26, 1938 in Leipzig. He attended the
High School "Wilhelmschule" in Kassel, in an experimental course with
emphasis on social studies and graduated in 1957 as the best student of
the year (with an additional exam with "Grosses Latinum" in 1958). From
the Spring semester 1957 he was a student of mathematics and physics at
the Faculty of Natural Sciences of Gottingen University. From the Spring
1960 he continued his studies at the University of Graz (Austria), at the
Faculty of Philosophy, taking his Diploma Thesis in theoretical physics,
with mathematics, philosophy and psychology as minors.
In the Fall term 1961-62 he was assistant to Prof. H. Lehmann at the
Institute of Theoretical Physics, University of Hamburg. He received his
PhD "mit Auszeichung" at the University of Graz in 1962 with the disser
tation "Analytische Eigenschaften der exakten Streuamplitude" which he
wrote under the direction of Prof. W. Zimmermann at Hamburg. After two
years, 1963-65, with the position of "Research Assistant" at the University
of Hamburg, he was from May 1, 1965 to July 31, 1967 at the Seminar for
Theoretical Physics, ETH, Zurich (Prof. M. Fierz and Prof. R. Jost).
In 1967-68, resp. 1968-69, he was a Research Associate, resp. an As
sistant Professor, at the Physics Department of Syracuse University. After
a period as Member of the Technical Staff at Bell Telephone Laborato
ries, Murray Hill, N. J., he was, in 1970, nominated Associate Professor at
Syracuse University.
He left Syracuse in 1972, to take over a position of Professor at the
Physics Department, University of Bielefeld, which he has held ever since.
Since 1973 he is also Honorarprofessor at the University of Graz. In 1980,
for professional reasons, he declined the offer of a chair in theoretical physics
at the University of Minister.
From 1989 to 1991 he was titular of the chair for Mathematical Physics
at the Universidade do Minho, Braga (Portugal) and since 1991 he holds
a chair at the Mathematics Department of the Universidade da Madeira,
Funchal (Portugal).
In 1980-91 he was given an "Akademie" -Fellowship by the Volkswagen
Foundation. He is the author of more than 150 research papers, on topics
vi
ranging from mathematical and theoretical physics, to mathematics, espe
cially the theory of stochastic processes, infinite dimensional analysis, the
theory of dynamical systems and their applications (in natural sciences and
engineering). He is also author of a very influential book on white noise
calculus and its applications and editor of 16 proceedings volumes.
His outstanding achievements in science are described more closely in
two articles (by S. Albeverio and T. Hida) in this volume. Let us stress
here that besides his research achievements Ludwig Streit has been very
successful in giving stimulus and furthering new research directions, creat
ing new research centres, organizing research workshops, and international
conferences. We mention the creation of the Research Centre BiBoS at the
University of Bielefeld (1984 - ), Bochum (1984 - 1997) and Bonn (1997
- ), the organization of a Series of Conferences "Bielefeld Encounters in
Mathematics and Physics" at Bielefeld University (started around 1978, of
which numerous Proceedings have appeared), the Research Years 1975-76,
"Mathematical Problems in Quantum Dynamics", 1983-84, "Project No. 2
in Mathematics and Physics" and "The sciences of complexity: from math
ematics and technology to a sustainable world", 2000-01 at the Center of
Interdisciplinary Research (ZiF) of the University of Bielefeld.
He has been Director of ZiF (1981-1985), International Adviser for
the International Institute for Advanced Studies at Kansai Science City
(Japan), has held executive positions in the International Association for
Mathematical Physics (1979-1985), IUPAP Commission for Mathematical
Physics (1981-1987), and he is member of several editorial boards of jour
nals and books.
He has given invited lectures at Universities in all continents, with re
peated long stays in Bulgaria, China, France, Italy, Japan, Philippines,
Russia, USA. Ludwig's "engagement" for science in Portugal deserves a
special mention. Starting with his nominations in Braga and Madeira, he
has developed an impressive activity of research and teaching, with an out
standing impact on the country's development of scientific research. Let us
mention here his creation of a school of Mathematical Physics in Madeira
with several PhD students at international level, his influence on other stu
dents in Portugal who came to Bielefeld and other Central European places
to do research work, his creation of the Research Centre "Centro de Cien-
cias Matematicas", his participation in the Committee of the Portuguese
Secretary of State for Research and Development for a national program in
astronomy, his organization of several workshops and international work
shops, conferences and Summer Schools in Madeira and Lisbon.
The contributions of Ludwig Streit for the development of science in
vii
Portugal were officially acknowledged and praised, at the time of the con
ference, by the Minister of Science of the Portuguese Government.
Ludwig Streit is an instant source of energy and inspiration in a broad
area of mathematics and physics and their many apphcations in natural
and social sciences. The contributions presented in this volume by stu
dents, friends, and coworkers reflect, at least partially, the broad interests
of Ludwig. The two first contributions by S. Albeverio and T. Hida are
particular in the sense that they have as a topic specific aspects of the
scientific work of Ludwig and the interaction with the authors over many
years. The other contributions, arranged alphabetically by authors, also
testify, in one way or another, the great influence of Ludwig in many areas
of mathematics, physics and their apphcations.
In the name of all friends and contributors, we wish Ludwig many more
years of good health and of successful pursuing of his outstanding activities,
in science and for the community.
This page is intentionally left blank
ix
Contents
Preface v
Ludwig Streit's list of publications xiii
Some themes of the scientific work of Ludwig Streit
S. Albeverio 1
Mathematics, Physics and Streit since 1975
T. Hida 8
Stochastic limit and interacting commutation relations
L. Accardi, I. Ya. Aref'eva and I. V. Volovich 18
De Rham complex over product manifolds: Dirichlet forms and
stochastic dynamics
S. Albeverio, A. Daletskii and Y. Kondratiev 37
Real time random walks on p-adic numbers
S. Albeverio and W. Karwowski 54
Characterization of test functions in CKS-space
JV. Asai, I. Kubo and H.-H. Kuo 68
Nonlinear Lie algebras in quantum physics and their interest in
quantum field theory
J. Beckers 79
Continuous percolation: tree approximation and most probable
clusters
Ph. Blanchard, G. F. Dell'Antonio, D. Gandolfo
and M. Sirugue-Collin 84
X
Rigged Hilbert space resonances and time asymmetric quantum
mechanics
A. Bohm and H. Kaldass 99
Q-Ising neural network dynamics: A comparative review of
various architectures
D. Bolle, G. Jongen and G. M. Shim 114
The relativistic Aharonov-Bohm-Coulomb problem: A path
integral solution
J. Bornales, C. C. Bernido and M. V. Carpio-Bemido 130
Statistical manifolds: The natural affine-metric structure of
probability theory
G. Burdet, Ph. Combe and H. Nencka 138
Brydges' operator in renormalization theory
P. Cartier and C. DeWitt-Morette 165
Fluctuation of the Bose-Einstein condensate in a trap
H. Ezawa, K. Nakamura, K. Watanabe and Y. Yamanaka 169
Time dependent and nonlinear point interactions
R. Figari 184
The Cole-Hopf and Miura transformations revisited
F. Gesztesy and H. Holden 198
Some models of nonideal Bose gas with Bose-Einstein condensate
R. Gielerak 215
Configuration spaces for self-similar random processes and
measures quasi-invariant under diffeomorphism groups
G. A. Goldin 228
Stochastic processes and the Feynman integral
Z. Haba 243
