Critical Dynamics, Stochastic Quantization and Supersymmetry

Abstract

For many years now, the deep connection between field theory and statistical mechanics has proved to be very powerful: for example, besides the study of critical equilibrium phenomena by the renormalisation group method^[1], it was known that critical dynamics could be formulated as an effective field theory^[2]. On the other hand in the last decade a new procedure for quantizing a field theory^[3] has been developed from an analogy with non equilibrium statistical mechanics. Based on the Langevin equation^[4], it is called Stochastic Quantization. Hence, the study of critical dynamics and stochastic quantization can be made from a field theoretic point of view which we adopt here.