A FDR-preserving field theory for interacting Brownian particles: one-loop theory and MCT

TL;DR

This paper develops a field theoretical approach for interacting Brownian particles that preserves FDR and time reversal symmetry, recovering known diffusion and mode coupling results at one-loop order.

Contribution

It introduces a modified auxiliary field method to ensure FDR preservation in the field theory of interacting Brownian particles.

Findings

Recovers the correct diffusion law without interactions.

Derives the standard mode coupling equation at one-loop order.

Ensures FDR and time reversal invariance in the theoretical framework.

Abstract

We develop a field theoretical treatment of a model of interacting Brownian particles. We pay particular attention to the requirement of the time reversal invariance and the fluctuation-dissipation relationship (FDR). The method used is a modified version of the auxiliary field method due originally to Andreanov, Biroli and Lefevre [J. Stat. Mech. P07008 (2006)]. We recover the correct diffusion law when the interaction is dropped as well as the standard mode coupling equation in the one-loop order calculation for interacting Brownian particle systems.