Superfield Formalism of Stochastic Quantization Method with Field-Dependent Kernels

TL;DR

This paper explores a superfield formalism for stochastic quantization with field-dependent kernels, demonstrating its equivalence to path-integral quantization and analyzing supersymmetry in the generating functional.

Contribution

It introduces a superfield approach to stochastic quantization with field-dependent kernels, clarifying its relation to path-integral methods and supersymmetry properties.

Findings

Superfield formalism clarifies stochastic quantization with field-dependent kernels.

Equivalence established between stochastic and path-integral quantization methods.

Supersymmetry of the generating functional is analyzed and confirmed.

Abstract

I consider a Langevin equation with field-dependent kernels and investigate supersymmetry of the stochastic generating functional constructed from the Langevin equation. Moreover I describe the stochastic generating functional in terms of a superfield. In the superfield formalism, it becomes clear that the stochastic quantization method with the field-dependent kernel is equivalent to the path-integral quantization method.