Renormalization of stochastically quantized field theories

Abstract

We discuss the renormalizability of stochastically quantized φ⁴ theory in four dimensions using the operator formalism of the Langevin equation developed by Namiki and Yamanaka. The operator formalism casts the Parisi Wu stochastic quantization scheme into a five-dimensional field theory. The usefulness of this approach over the one based directly on the Langevin equation is brought out for discussion of renormalization. We propose a new regularization scheme for the stochastic diagrams and use it to compute the renormalization constants and counter terms for the φ⁴ theory to second order in the coupling constant.