Mathematical Physics X: Proceedings of the Xth Congress on Mathematical Physics, Held at Leipzig, Germany, 30 July – 9 August, 1991

510 Pages·1992·35.043 MB·English

by  R. de la Llave (auth.), Prof. Dr. Konrad Schmüdgen (eds.)

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Gottfried Wilhelm Leibniz (1646-1716) in front of the lecture hall (left) of the lAMP
Congress. Leibniz was a student at the University of Leipzig. The university's main
building may be seen in the background.
K. Schmtidgen (Ed.)
Mathematical Physics X
Proceedings of the Xth Congress
on Mathematical Physics
Held at Leipzig, Germany, 30 July - 9 August 1991
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Prof. Dr. Konrad Schmiidgen
Fachbereich Mathematik
Universitat Leipzig
Augustusplatz 10
0-7010 Leipzig, FRG
ISBN-13: 978-3-642-77305-1 e-ISBN-13: 978-3-642-77303-7
DOl: 10.1007/978-3-642-77303-7
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© Springer-Verlag Berlin Heidelberg 1992
So/kover reprint of the hardcover I st edition 1992
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Preface
This volume contains the proceedings of the Xth Congress of the Interna
tional Association of Mathematical Physics, held at the University of Leipzig
from 30 July until 9 August 1991. There were more than 400 participants,
from 29 countries, making it a truly international gathering.
The congress had the support of the Deutsche Forschungsgemeinschaft,
the European Economic Community, the International Association of Math
ematical Physics, the International Mathematical Union and the Interna
tional Union of Pure and Applied Physics. There were also sponsors from in
dustry and commerce: ATC Mann, Deutsche Bank AG, Miele & Cie GmbH,
NEC Deutschland GmbH, Rank Xerox, Siemens AG and Stiftungsfonds
IBM Deutschland. On behalf of the congress participants and the members
of the International Association of Mathematical Physics, I would like to
thank all these organisations for their very generous support.
The congress took place under the auspices of the Ministerp6isident des
Freistaates Sachsen, K. Biedenkopf.
The conference began with an address by A. Uhlmann, Chairman of
the Local Organizing Committee. This was followed by speeches of welcome
from F. Magirius, City President of Leipzig; C. Weiss, Rector of the Uni
versity of Leipzig; and A. Jaffe, President of the International Association
of Mathematical Physics.
The main part of the scientific program consisted of 18 plenary lectures
and 13 special sessions. The plenary speakers were invited by the scientific
Organizing Committee, chaired by W. Thirring (Vienna), to present reviews
of their respective fields, accessible to all participants. The committee also
chose the session organizers. The special sessions comprised both invited
lectures in topical sessions and shorter contributions, invited and submitted,
in poster sessions. The session organizers were responsible for the program
and are also responsible for the choice of contributions to the proceedings
from their sessions.
Two seminars were organized during the conference, one on "Geomet
ric phase" by A. Bolun (Austin) and one on "Energy levels and moments
of the Schrodinger equation and relativistic generalizations" by A. Martin
(Geneva). There was also a particularly lively round table discussion "On
the foundations of quantum mechanics" directed by A. Wightman (Prince
ton), with contributions from S. Goldstein (Rutgers), R. Haag (Hamburg),
R. Omnes (Paris), H. Primas (Zurich) and W. Zurek (Los Alamos).
VI Preface
Additionally, a free poster session was held on Sunday. A list of these
posters and their authors is included in these proceedings.
As at all such congresses, a great deal of work was done by many people.
In particular, the congress could not have taken place without the dedicated
work of members of the Mathematical Physics groups at the Department of
Mathematics and the Department of Physics. Their work began more than
one year ago, and culminated during the congress itself. Special thanks must
also go to the staff of the N aturwissenschaftlich-Theoretisches Zentrum and
to K. Scharnhorst, Secretary INTSEM.
Finally, I would like to express my personal thanks to R. Becker, J.
Dittmann and R. Schildt for their assistance in preparing these proceedings,
in particular, for their help in formatting, proofreading and even retyping
manuscripts.
Leipzig, K. Schmiidgen
November 1991
Contents
Preface .................................................... V
Contents ................................................... VII
Committees ................................................ XI
List of Participants .......................................... XIII
Part I Plenary Lectures
R. de la Llave: Recent Progress in Classical Mechanics ........... 3
B. Zumino: Introduction to the Differential Geometry of
QuantuIll Groups ........................................... 20
B. V. Chirikov: Chaotic Quantum Systems ...................... 34
D. Ruelle: Dynamical Zeta Functions: Where Do They Come
From and What Are They Good For? ......................... 43
L.A. Bunimovich: Billiard-Type Systems with Chaotic Behaviour
and Space-Time Chaos ...................................... 52
L.A. Pastur: Statistical Physics and Spectral Theory of Disordered
Systems: Some Recent Developments .......................... 70
F. Martinelli: Low Temperature Stochastic Spin Dynamics:
Metastability, Convergence to Equilibrium and Phase Segregation. 87
S.R.S. Varadhan: Entropy Methods in Hydrodynamical Scaling ... 103
Y.!. Manin: Quantum Groups and Non-Commutative Differential
Geometry .................................................. 113
L.D. Faddeev: Hamiltonian Methods in Conformal Field Theory 123
K. Fredenhagen: On the General Theory of Quantized Fields 136
J.P. Solovej: Atomic and Molecular Structure - A Renormalized
Picture - .................................................. 153
J. Frohlich, U.M. Studer: Gauge Invariance in Non-Relativistic
Many-Body Theory ......................................... 165
G.M. Graf Asymptotic Completeness for N-Body Quantum
Systems ................................................... 174
R. Jackiw: Self-Dual Chern-Simons Solitons .................... 184
S. Klainerman: Mathematical Theory of Classical Fields and
General Relativity .......................................... 213
J. Cuntz: Representations of Quantized Differential Forms in
Non-Commutative Geometry ................................. 237
VIII Contents
Part II Session Lectures
Section 1: Analysis on Manifolds and Classical Mechanics
W. Craig, C.E. Wayne: Solutions of Nonlinear Wave Equations
and Localization Theory ..................................... 256
V. V. Trofimov: Connections on Symplectic Manifolds and
Characteristic Classes of Hamiltonian Systems .................. 262
Ch. GoLe: Symplectic Twist Maps and the Theorem of Conley-
Zehnder for General Cotangent Bundles ......... . . . . . . . . . . . . . . 265
S. Dostoglou, D. Salamon: Floer Homology for Mapping Cylinders 269
Section 2: Quantum Groups and Non-Commutative
Differential Geometry
J. Lukierski: K.-Deformation of (Super )Poincare Algebra ......... 274
A. Jaffe: Quantum Physics as Non-Commutative Geometry 281
T. Masuda, Y. N akagami: An Operator Algebraic Framework for
the Duality of Quantum Groups .............................. 291
Section 3: Chaotic Quantum Systems
P.M. Bleher: Distribution of Energy Levels in Quantum Systems
with Integrable Classical Counterpart. Rigorous Results .......... 298
D. Voic'ulescu: Entropy-Invariants of Dynamical Systems and
Perturbations of Operators ................................... 303
M. Klein, A. Knauf. Chaotic Motion in Coulombic Potentials ..... 308
H.R. Jauslin, J.L. Lebowitz: Generalized Floquet Operator for
Quasiperiodically Driven Quantum Systems .................... 313
Section 4: Equilibrium Statistical Mechanics
L.R. G. Fontes: Magnetization and Slow Decay of Correlations in
Continuum 1/r2 Ising Models ................................ 318
A. Klein: Existence of the Kosterli tz-Thouless Phase for Two
Dimensional Coulomb Gases at Inverse Temperatures above 81r ... 322
R.L. Dobrushin, S.B. Shlosman: Large Deviation Behavior of
Statistical Mechanics Models in the Multiphase Regime .......... 328
Section 5: Classical Dynamical Systems and Random
Perturbations
Y. Kifer: A Variational Approach to the Random Diffeomorphisms
Type Perturbations of a Hyperbolic Diffeomorphism ............. 334
M.L. Blank: Chaotic Mappings and Stochastic Markov Chains 341
Section 6: Disordered Systems
A. Klein: Quantum Spin Systems in a Random Environment 348
J. Wehr: Rounding Effects in Systems with Static Disorder ....... 355
Contents IX
Section 7: Nonequilibrium Statistical Mechanics
H.-T. Yau: Derivation of Euler Equation from Hamiltonian
Systems with Negligible Random Noise ........................ 360
M. Bramson, J.L. Lebowitz: The Spatial Structure in Diffusion
Limited Two-Particle Reactions ............................... 364
D.A. Dawson, J. Gurtner: Multilevel Models of Interacting
Diffusions and Large Deviations ..... . . . . . . . . . . . . . . . . . . . . . . . . . 370
Section 8: General Theory of Quantized Fields
J. Bros: Fields, Particles and Analyticity: Recent Results ........ 376
B.S. Kay: Quantum Field Theory in Curved Spacetime .......... 383
K.-H. Rehren: Charges in Quantum Field Theory ............... 388
A.S. Wightman: Three Exactly Soluble Quantum Field Theory
Models in 2-, 3- and 4-Dimensional Space Time and Some General
Questions They Suggest ..................................... 393
H.J. Borchers: CPT- and Lorentz-Transformations in Two-
Dimensional Quantum Field Theory ........................... 399
J. Roberts: The Concept of Spontaneously Broken Symmetry and
a New Approach to Goldstone's Theorem ...................... 404
Section 9: Nonrelativistic Quantum Mechanics
(Stationary)
C.L. Fefferman, L.A. Seco: On the Atomic Energy Asymptotics 408
Section 10: Special Systems in Quantum Field Theory
P.A. Faria da Veiga: Existence of the Schwinger Functions of
the Three-Dimensional Gross-Neveu Model .................... 420
H. Grosse: Progress in Completely Integrable Models of Quantum
Field Theory ............................................... 423
Section 11: Scattering Theory, Inverse Problems
A.!, Nachman: Inverse Scattering at Fixed Energy .............. 434
D. Robert: Semi-Classical and High-Energy Asymptotics of the
Scattering Phase for Perturbations of Elliptic Operators ......... 442
A. Jensen, S. Nakam'ura: On the Mapping Properties of the
Wave Operators in Scattering Theory .......................... 447
Section 12: Conformal and Topological Field Theory
A. W. Wipf Reduction of Kac-Moody Systems ................. 452
L.K. Hadjiivanov, Y.S. Stanev, I. T. Todorov: Quantum Symmetry
of Rational Conformal Models ................................ 457
X Contents
Section 13: General Relativity and Classical Field Theory
B. G. Schmidt: Quasi-Normal Modes of the Schwarzschild
Space-Time ................................................ 464
A.D. Rendall: The Initial Value Problem for Self-Gravitating
Fluid Bodies ................................. . . . . . . . . . . . . . . 470
Poster Session and Program
Poster Session .............................................. 477
Prograln ................................................... 488