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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.
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Inhaltsangabe
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 DynamicalSystems 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.- Reduction of Kac-Moody Systems.- Quantum Symmetry of Rational Conformal Models.- Section 13: General Relativity and Classical Field Theory.- Quasi-Normal Modes of the Schwarzschild Space-Time.- The Initial Value Problem for Self-Gravitating Fluid Bodies.- Poster Session and Program.- Poster Session.- Program.
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 DynamicalSystems 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.- Reduction of Kac-Moody Systems.- Quantum Symmetry of Rational Conformal Models.- Section 13: General Relativity and Classical Field Theory.- Quasi-Normal Modes of the Schwarzschild Space-Time.- The Initial Value Problem for Self-Gravitating Fluid Bodies.- Poster Session and Program.- Poster Session.- Program.
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