Quantum-field-theoretical techniques for stochastic representation of quantum problems

TL;DR

This paper introduces quantum-field-theoretical methods to transform quantum problems into stochastic equations, providing a consistent approach even when phase-space techniques fail to produce Fokker-Planck equations.

Contribution

It presents a novel application of QFT techniques for stochastic representation of quantum problems, extending the scope beyond phase-space methods.

Findings

QFT techniques match phase-space results when Fokker-Planck equations exist

QFT yields stochastic difference equations when phase-space methods fail

Provides a unified framework for stochastic quantum problem representation

Abstract

We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation, the QFT techniques nevertheless yield stochastic difference equations in discretised time.