Stochastic Quantization of Topological Field Theory: Generalized Langevin Equation with Memory Kernel

TL;DR

This paper applies stochastic quantization with a memory kernel to topological field theories, demonstrating convergence in Abelian Chern-Simons theory regardless of the coefficient's nature.

Contribution

It introduces a generalized Langevin equation with a memory kernel for stochastic quantization of topological field theories, ensuring convergence in Abelian Chern-Simons theory.

Findings

Convergence of the stochastic quantization procedure regardless of the Chern-Simons coefficient

Extension of stochastic quantization methods to topological field theories with memory effects

Validation in the context of Abelian Chern-Simons theory

Abstract

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient.