Stochastic Analysis and Applications in Physics

The intensive exchange between mathematicians and users has led in recent years to a rapid development of stochastic analysis. Of the users, the physicists form perhaps the most important group, giving direction to the mathematicians' research and providing a source of intuition. White noise analysis has emerged as a viable framework for stochastic and infinite dimensional analysis. Another growth area is the theory of stochastic partial differential equations. Gauge field theories are attracting increasing attention. Dirichlet forms provide a fruitful link between the mathematics of Markov processes and the physics of quantum systems. The deterministic--stochastic interface is addressed, as are Euclidean quantum mechanics, excursions of diffusions and the convergence of Markov chains to thermal states. Front Matter....Pages i-xv Infinite Dimensional Diffusions, Markov Fields, Quantum Fields and Stochastic Quantization....Pages 1-34 Burgers Equation Forced by Conservative or Nonconservative Noise....Pages 35-44 Statistical Properties of Piecewise Expanding Maps of the Interval....Pages 45-57 Euclidean Quantum Mechanics. An outline....Pages 59-97 Analysis on Loop Groups....Pages 99-118 White Noise Analysis and Applications....Pages 119-131 Computer Stochastics in Scalar Quantum Field Theory....Pages 133-191 Brownian Motion Over a Kahler Manifold and Elliptic Genera of Level N....Pages 193-217 On Lyapounov Stability Theorems for Stochastic (Deterministic) Evolution Equations 1 ....Pages 219-237 Stochastic Techniques in Condensed Matter Physics....Pages 239-281 Stochastic Partial Differential Equations and Applications to Hydrodynamics....Pages 283-305 White Noise Approach to Parabolic Stochastic Partial Differential Equations....Pages 307-327 Colombeau Generalized Functions and Stochastic Analysis....Pages 329-349 Constructive Field Theoretic Methods and Stochastic Partial Differential Equations....Pages 351-387 Quantum Yang-Mills Theory on Compact Surfaces....Pages 389-403 Entropy and KMS norms....Pages 405-413 An Introduction to White Noise Analysis....Pages 415-439 Excursion Measures for One-Dimensional Time-Homogeneous Diffusions with Inaccessible and Accessible Boundaries....Pages 441-454 The intensive exchange between mathematicians and users has led in recent years to a rapid development of stochastic analysis. This text describes some of its applications in physics including: white noise analysis; gauge field theories; and euclidean quantum mechanics. Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993