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

The plenary lectures in this volume give a fairly complete overview of present research in mathematical physics. The contributions cover classical mechanics on manifolds, non-commutative differential geometry and quantum groups, chaotic quantum systems, various topics in equilibrium and non-equilibrium statistical mechanics, quantum field theory, including topological field theory, and classical field theory.

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The plenary lectures in this volume give a fairly complete overview of present research in mathematical physics. The contributions cover classical mechanics on manifolds, non-commutative differential geometry and quantum groups, chaotic quantum systems, various topics in equilibrium and non-equilibrium statistical mechanics, quantum field theory, including topological field theory, and classical field theory.
Content:
Front Matter....Pages I-XX
Front Matter....Pages 1-1
Recent Progress in Classical Mechanics....Pages 3-19
Introduction to the Differential Geometry of Quantum Groups....Pages 20-33
Chaotic Quantum Systems....Pages 34-42
Dynamical Zeta Functions: Where Do They Come from and What Are They Good for ?....Pages 43-51
Billiard-Type Systems with Chaotic Behaviour and Space-Time Chaos....Pages 52-69
Statistical Physics and Spectral Theory of Disordered Systems: Some Recent Developments....Pages 70-86
Low Temperature Stochastic Spin Dynamics: Metastability, Convergence to Equilibrium and Phase Segregation....Pages 87-102
Entropy Methods in Hydrodynamical Scaling....Pages 103-112
Quantum Groups and Non-commutative Differential Geometry....Pages 113-122
Hamiltonian Methods in Conformal Field Theory....Pages 123-135
On the General Theory of Quantized Fields....Pages 136-152
Atomic and Molecular Structure....Pages 153-164
Gauge Invariance in Non-Relativistic Many-Body Theory....Pages 165-173
Asymptotic Completeness for N-Body Quantum Systems....Pages 174-183
Self-Dual Chern—Simons Solitons....Pages 184-212
Mathematical Theory of Classical Fields and General Relativity....Pages 213-236
Representations of Quantized Differential Forms in Non-Commutative Geometry....Pages 237-251
Front Matter....Pages 253-253
Solutions of Nonlinear Wave Equations and Localization Theory....Pages 256-261
Connections on Symplectic Manifolds and Characteristic Classes of Hamiltonian System....Pages 262-264
Symplectic Twist Maps and the Theorem of Conley-Zehnder for General Cotangent Bundles....Pages 265-268
Front Matter....Pages 253-253
Floer Homology for Mapping Cylinders....Pages 269-271
Quantum Physics as Non-Commutative Geometry....Pages 274-280
An Operator Algebraic Framework for the Duality of Quantum Groups....Pages 274-280
Distribution of Energy Levels in Quantum Systems with Integrable Classical Counterpart. Rigorous Results....Pages 281-290
Entropy-Invariants of Dynamical Systems and Perturbations of Operators....Pages 291-295
Chaotic Motion in Coulombic Potentials....Pages 298-302
Generalized Floquet Operator for Quasiperiodically Driven Quantum Systems....Pages 303-307
Existence of the Kosterlitz-Thouless Phase for Two-Dimensional Coulomb Gases at Inverse Temperatures above 8?....Pages 308-312
Large Deviation Behavior of Statistical Mechanics Models in the Multiphase Regime....Pages 313-316
A Variational Approach to the Random Diffeomorphisms Type Perturbations of a Hyperbolic Diffeomorphism....Pages 318-321
Chaotic Mappings and Stochastic Markov Chains....Pages 318-321
Quantum Spin Systems in a Random Environment....Pages 322-327
Rounding Effects in Systems with Static Disorder....Pages 328-332
Derivation of the Euler Equation from Hamiltonian Systems with Negligible Random Noise....Pages 334-340
The Spatial Structure in Diffusion Limited Two-Particle Reactions....Pages 341-345
Multilevel Models of Interacting Diffusions and Large Deviations....Pages 348-354
Fields, Particles and Analyticity: Recent Results or 30 Goldberg ...(er) Variations on B.A.C.H. where B=Bethe Salpeter Equation, A=Axiomatic Field Theory C=Complex Variables and H=Harmonic Analysis....Pages 355-358
Quantum Field Theory in Curved Spacetime....Pages 360-363
Front Matter....Pages 364-369
Charges in Quantum Field Theory....Pages 370-374
Three Exactly Soluble Quantum Field Theory Models in 2-,3- and 4-Dimensional Space Time and Some General Questions They Suggest....Pages 376-382
CPT- and Lorentz-Transformations in Two-Dimensional Q.F.T.....Pages 383-387
The Concept of Spontaneously Broken Symmetry and a New Approach to Goldstone’s Theorem....Pages 253-253
On the Atomic Energy Asymptotics....Pages 388-392
Existence of the Schwinger Functions of the Three-Dimensional Gross-Neveu Model....Pages 393-398
Progress in Completely Integrable Models of Quantum Field Theory....Pages 399-403
Inverse Scattering at Fixed Energy....Pages 404-406
Semi-Classical and High Energy Asymptotics of the Scattering Phase for Perturbations of Elliptic Operators....Pages 408-418
On the Mapping Properties of the Wave Operators in Scattering Theory....Pages 420-422
Reduction of Kac-Moody Systems....Pages 423-431
Quantum Symmetry of Rational Conformal Models....Pages 434-441
Quasi-Normal Modes of the Schwarzschild Space-Time....Pages 442-446
The Initial Value Problem for Self-Gravitating Fluid Bodies....Pages 447-450
Back Matter....Pages 452-456
....Pages 457-462