Mathematical Problems in Theoretical Physics

Inhaltsverzeichnis

• Lattice instantons: What they are and why they are important.
• Gauge fields on the lattice.
• Lattice gauge theories.
• Some frontiers in constructive quantum field theory and equilibrium statistical mechanics.
• New proofs of long range order.
• Number of phases in one component ferromagnets.
• A survey of local cohomology.
• Operator algebras and statistical mechanics.
• Foundations of equilibrium quantum statistical mechanics.
• Unbounded derivations of C*-algebras and corresponding dynamics.
• to the flow of weights on factors of type III.
• The von Neumann algebra of a foliation.
• Nuclearity and the C*-algebraic flip.
• On the Connes spectrum of simple C*-dynamical systems.
• Quantum field theory of massless particles and scattering theory.
• Scattering theory in quantum mechanics and asymptotic completeness.
• Static solitons in more than one dimension.
• Geometry of Yang-Mills fields.
• Periodic solitons and algebraic geometry.
• Yang--Mills equations as inverse scattering problem.
• Nonlinear evolution equations solvable by the inverse spectral transform.
• Quantization of particle-like solutions in field theory.
• Topics in infinite dimensional analysis.
• Mathematical foundations of the renormalization group method in statistical physics.
• On the renormilization group for the hierarchical model.
• Fluctuationes in Curie-Weiss exemplis.
• On the problem of the mathematical foundation of the Gibbs postulate ie classical statistical mechanics.
• Dynamical systems with turbulent behavior.
• Generic properties of Navier-Stokes equations.
• A limit theorem for turbulent diffusion.
• Many particle scattering aitlitudes.
• A Remark on equations of motion in asymptotically free theories.
• Short-distance expansion for products of current-like operators.
• The use of exterior forms in field theory.
• On extensions of flows in the presence of sets of singularities.
• On the uniqueness of the equilibrium state for plane rotators.
• A geometric approach to the solution of conformal invariant field equations.
• Stability, detailed balance and KMS condition for quantum systems.
• Stochasticity and irreversibility in infinite mechanical systems.
• Why the KMS states?.
• A comment to the talk by E. Seiler.