Renormalization group equations in the stochastic quantization scheme

Abstract

We show that there exists a remarkable link between the stochastic quantization and the theory of critical phenomena and dynamical statistical systems. In the stochastic quantization of a field theory, the stochastic Green functions converge to the quantum ones when the fictitious time goes to infinity. We therefore use the typical techniques of the Renormalization Group equations, developed in the framework of critical phenomena, to discuss some features of the convergence of the stochastic theory. We are also able, in this way, to compute some dynamical critical exponents and give new numerical valuations for them.