# On Stochastic Quantisation of Supersymmetric Theories

## TL;DR

This paper explores how to reconcile stochastic quantization with space supersymmetry in supersymmetric theories, demonstrating that the stochastic process converges to the standard path integral regardless of certain kernel choices.

## Contribution

It introduces supersymmetry-compatible kernels in stochastic quantization for N=2 supersymmetric quantum mechanics, ensuring convergence to the path integral.

## Key findings

- Kernels depend on a parameter M that influences stochastic evolution
- The infinite stochastic time limit is independent of M
- Compatibility of stochastic TQFT supersymmetry with space supersymmetry is established

## Abstract

We explain how stochastic TQFT supersymmetry can be made compatible with space supersymmetry. Taking the case of N=2 supersymmetric quantum mechanics, (the proof would be the same for the Wess-Zumino model), we determine the kernels that ensure the convergence of the stochastic process toward the standard path integral, under the condition that they are covariant under supersymmetry. They depend on a massive parameter M that can be chosen at will and modifies the course of the stochastic evolution, but the infinite stochastic time limit of the correlation functions is in fact independent on the choice of M.