Stochastic quantization with discrete fictitious time

TL;DR

This paper introduces a novel stochastic quantization method using discrete fictitious time, which accurately reproduces quantum field theory correlations without continuum limits, demonstrated through a zero-dimensional model.

Contribution

It proposes a new stochastic quantization approach with discrete fictitious time, avoiding continuum limits and validated through perturbative and numerical tests.

Findings

Method reproduces quantum correlations without continuum limit.

Validated in a zero-dimensional toy model.

Shows potential for more efficient quantum field simulations.

Abstract

We present a new approach to stochastic quantization \`a la Parisi-Wu with a discrete fictitious time. The noise average is modified by weights, which results in the equivalence in the large time limit to the correlation function of the corresponding quantum field theory {\it without taking any continuum limit of fictitious time}. We test our method in a zero-dimensional toy model both perturbatively and numerically.