Stochastic quantization

Stochastic quantization provides a novel and interesting connection between quantum field theory and statistical mechanics, with new applications also in numerical simulations of field theories. This review article tries to present as broad as possible the most relevant features of the Parisi-Wu approach of stochastic quantization. It covers scalar, gauge, tensor and string field theories, it discusses fermions and explores the intrinsic connection of stochastic quantization to supersymmetry. Further topics are the large N-limit, stochastic quantization in Minkowski space and stochastic regularization. Finally we describe some rather recent developments concerning the numerical possibilities associated with stochastic quantization.