Mathematical Physics X

Proceedings of the Xth Congress on Mathematical Physics, Held at Leipzig, Germany, 30 July - 9 August, 1991
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The plenary lectures in this volume give a fairly complete overview of the present research in mathematical physics. The book addresses researchers and advanced students in both physics and mathematics.
The plenary lectures in this volume give a fairly complete overview of the present research in mathematical physics. The book addresses researchers and advanced students in both physics and mathematics.
I Plenary Lectures.- Recent Progress in Classical Mechanics.- to the Differential Geometry of Quantum Groups.- Chaotic Quantum Systems.- Dynamical Zeta Functions: Where Do They Come From and What Are They Good For?.- Billiard-Type Systems with Chaotic Behaviour and Space-Time Chaos.- Statistical Physics and Spectral Theory of Disordered Systems: Some Recent Developments.- Low Temperature Stochastic Spin Dynamics: Metastability, Convergence to Equilibrium and Phase Segregation.- Entropy Methods in Hydrodynamical Scaling.- Quantum Groups and Non-Commutative Differential Geometry.- Hamiltonian Methods in Conformal Field Theory.- On the General Theory of Quantized Fields.- Atomic and Molecular Structure - A Renormalized Picture -.- Gauge Invariance in Non-Relativistic Many-Body Theory.- Asymptotic Completeness for N-Body Quantum Systems.- Self-Dual Chern-Simons Solitons.- Mathematical Theory of Classical Fields and General Relativity.- Representations of Quantized Differential Forms in Non-Commutative Geometry.- II Session Lectures.- Section 1: Analysis on Manifolds and Classical Mechanics.- Solutions of Nonlinear Wave Equations and Localization Theory.- Connections on Symplectic Manifolds and Characteristic Classes of Hamiltonian Systems.- Symplectic Twist Maps and the Theorem of Conley-Zehnder for General Cotangent Bundles.- Floer Homology for Mapping Cylinders.- Section 2: Quantum Groups and Non-Commutative Differential Geometry.- ?-Deformation of (Super)Poincaré Algebra.- Quantum Physics as Non-Commutative Geometry.- An Operator Algebraic Framework for the Duality of Quantum Groups.- Section 3: Chaotic Quantum Systems.- Distribution of Energy Levels in Quantum Systems with Integrable Classical Counterpart. Rigorous Results.- Entropy-Invariants of Dynamical Systems and Perturbations of Operators.- Chaotic Motion in Coulombic Potentials.- Generalized Floquet Operator for Quasiperiodically Driven Quantum Systems.- Section 4: Equilibrium Statistical Mechanics.- Magnetization and Slow Decay of Correlations in Continuum 1/r2 Ising Models.- Existence of the Kosterlitz-Thouless Phase for Two-Dimensional Coulomb Gases at Inverse Temperatures above 8?.- Large Deviation Behavior of Statistical Mechanics Models in the Multiphase Regime.- Section 5: Classical Dynamical Systems and Random Perturbations.- A Variational Approach to the Random Diffeomorphisms Type Perturbations of a Hyperbolic Diffeomorphism.- Chaotic Mappings and Stochastic Markov Chains.- Section 6: Disordered Systems.- Quantum Spin Systems in a Random Environment.- Rounding Effects in Systems with Static Disorder.- Section 7: Nonequilibrium Statistical Mechanics.- Derivation of Euler Equation from Hamiltonian Systems with Negligible Random Noise.- The Spatial Structure in Diffusion Limited Two-Particle Reactions.- Multilevel Models of Interacting Diffusions and Large Deviations.- Section 8: General Theory of Quantized Fields.- Fields, Particles and Analyticity: Recent Results.- Quantum Field Theory in Curved Spacetime.- Charges in Quantum Field Theory.- Three Exactly Soluble Quantum Field Theory Models in 2-, 3- and 4-Dimensional Space Time and Some General Questions They Suggest.- CPT- and Lorentz-Transformations in Two-Dimensional Quantum Field Theory.- The Concept of Spontaneously Broken Symmetry and a New Approach to Goldstone's Theorem.- Section 9: Nonrelativistic Quantum Mechanics (Stationary).- On the Atomic Energy Asymptotics.- Section 10: Special Systems in Quantum Field.- Existence of the Schwinger Functions of the Three-Dimensional Gross-Neveu Model.- Progress in Completely Integrable Models of Quantum Field Theory.- Section 11: Scattering Theory, Inverse Problems.- Inverse Scattering at Fixed Energy.- Semi-Classical and High-Energy Asymptotics of the Scattering Phase for Perturbations of Elliptic Operators.- On the Mapping Properties of the Wave Operators in Scattering Theory.- Section 12: Conformai and Topological Field Theory
th This volume contains the proceedings of the X 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.