Fourth order full quantum correlations from a Langevin-Schwinger-Dyson equation

TL;DR

This paper extends the stochastic source method to higher-order quantum correlations using Langevin-Schwinger-Dyson equations, enabling analysis of nonlinear quantum fluctuation dynamics beyond second order.

Contribution

It introduces a novel approach to compute third and fourth order quantum correlations via stochastic sources in higher effective action frameworks.

Findings

Successfully derived third and fourth order correlations

Demonstrated the method's applicability to nonlinear quantum fluctuation analysis

Provided a simpler way to investigate complex quantum dynamics

Abstract

It is well known that some quantum and statistical fluctuations of a quantum field may be recovered by adding suitable stochastic sources to the mean field equations derived from the Schwinger-Keldysh (Closed-time-path) effective action. In this note we show that this method can be extended to higher correlations and higher (n-particle irreducible) effective actions. As an example, we investigate three and fourth order correlations by adding stochastic sources to the Schwinger - Dyson equations derived from the 2-particle irreducible effective. This method is a simple way to investigate the nonlinear dynamics of quantum fluctuations.