Probabilistic Methods in Quantum Field Theory and Quantum Gravity -

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Résumé :
From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity was held at l'Institut d'Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan? tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.

Sommaire:
Lectures.- Some Stochastic Techniques in Quantization, New Developments in Markov Fields and Quantum Fields.- Random Surfaces: A Non-perturbative Regularization of Strings?.- From Lattice Gauge Theory Towards Gravity.- Geometric Continuum Regularization of Quantum Field Theory.- Quantization = Geometry + Probability.- Simulation of Staggered Fermions by Polymer Algorithms.- All Gauge Orbits and Some Gribov Copies Encompassed by the Gribov Horizon.- Lattice Gauge Theories.- Beyond the Gribov Horizon in the Femto Universe.- The O (N)-symmetric Non-linear ?-model to Three Leading Orders in 1/N.- Simulations of Lattice QCD with Dynamical Fermions.- Stochastic Overrelaxation Algorithms and Critical Slowing down.- Slave Equations for Connected Correlation Functions.- The Monomer-Dimer Algorithm and QCD at Finite Density.- The Theory of Hybrid Stochastic Algorithms.- Numerical Investigation of Four-Dimensional Field Theories.- Quantum Gravity.- Probabilit?, Time and Gravity.- Simplicial Quantum Gravity from Two to Four Dimensions.- BRS Symmetry in Stochastic Quantization of the Gravitational Field.- Solved and Unsolved Problems in the Stochastic Quantization of Gravity.- Brs Symmetry and Supersymmetry in Stochastic Quantization.- Hidden BRST Symmetry and Large N.- On Gauge Invariances in Stochastic Quantization.- Critical Dynamics, Stochastic Quantization and Supersymmetry.- Renormalization in Stochastic Quantization and Supersymmetry.- Random Walks and Random Surfaces.- Random Walk Representation of Propagators for Particles with Spin.- The Critical Behavior of a Nontrivial Random Surface Model.- Random Surfaces with Ising Spins.- The Use of Fourier Acceleration in the Langevin Simulation of Random Surfaces.- Miscellany.- Path Integral Approach to Classical Mechanics.- AnApproach to Quantum Field Theory Through Stochastic Equations.- Remarks on the Renormalisation of Fermions Coupled to Gauge Fields in the Zwanziger Gauge.- The Parisi-Wu Method and Quantum Chaos.- Participants.