Functional Integration Theory and Applications

The idea of the workshop on Functional Integration, Theory and Applications, held in Louvain-Ia-Neuve from November 6 to 9 1979, was to put in close and informal contact, during a few days, active workers in the field. There is no doubt now that functional integration is a tool that is being applied in all branches of modern physics. Since the earlier works of Dirac and Feynman enormous progress has been made, but unfortunately we lack still a unifying and rigo­ rous mathematical framework to account for all the situations in which one is interested. We are then in presence of a rapid­ ly changing field in which new achievements, proposals, and points of view are the normal pattern. Considering this state of affairs we have decided to order the articles starting from the more fundamental and ambitious from the point of view of mathematical rigour, followed by ar­ ticles in which the main interest is the application to con­ crete physical situations. It is obvious that this ordering should not be taken too seriously since in many cases there will be an interplay of both objects.

Anticommutative Integration.- Stationary Phase for the Feynman Integral and Trace Formula.- White Noise Analysis and the Feynman Integral.- Feynman Formula and Poisson Processes for Gentle Perturbations.- The Classical Limit of Quantum Mechanics in a Curved Space Background.- Integration in Hilbert Space and Quantum Theory.- Path Integrals for Affine Variables.- Path Integrals over Coherent States.- Path Integrals, Coherent States, and Geometric Quantization.- Translational Invariance in Feynman-Type Integrals.- Canonical Versus Functional Methods in Quantum Mechanics and Field Theory.- A Stochastic Description of Tunneling in Quantum Mechanics.- Dependence of the Feynman Path Integral on Discretization: The Case of a Spinless Particle in an External Electromagnetic Field.- Semiclassical Expansions on Riemannian Manifolds.- Quantization in Curved Spaces: Functional Integration and the Quantum Action Principle on Riemannian Geometries.- Intrinsic Path Integral Solution to the Fokker-Planck Equation.- Path Integrals, Composite Operators and Mode Coupling.- Onsager-Machlup Function of Nonlinear Non-Equilibrium Thermodynamics.- The Onsager-Machlup Lagrangian and the Optimal Control for Diffusion Processes.- Feynman’s Approach to the Polaron Problem Generalized to Arbitrary Quadratic Actions.- Nonlinear D.C.-Conductivity in Polar Semiconductors.- The Uses of Instantons for Diffusion in Bistable Potentials.- Metastable Phases and Perturbation Expansions.- Participants.