Stochastic quantization of massive fermions

TL;DR

This paper demonstrates that solutions to a Langevin equation for massive fermions produce correlators identical to Euclidean Quantum Field Theory Schwinger functions, linking stochastic processes with quantum field theory.

Contribution

It establishes a connection between stochastic Langevin solutions and Euclidean QFT correlators for massive fermions, providing a new approach to quantum field analysis.

Findings

Correlators from Langevin solutions match Schwinger functions.

Assumption of solution existence is key to the result.

Bridges stochastic methods with quantum field theory.

Abstract

We consider a general solution of the Langevin equation describing massive fermions to an appropriate boundary problem. Assuming existence of such solution we show that its correlators coincide with the Schwinger functions of corresponding Euclidean Quantum Field Theory.