Mode coupling theory in the FDR-preserving field theory of interacting Brownian particles

TL;DR

This paper develops a renormalized perturbation theory for interacting Brownian particles that maintains the fluctuation-dissipation relation and results in a mode coupling theory consistent with established models.

Contribution

It introduces a FDR-preserving field theory framework that yields a closed density correlation equation matching standard mode coupling theory.

Findings

The theory preserves the fluctuation-dissipation relation at each order.

The one-loop approximation produces a density correlation equation identical to standard MCT.

Provides a new theoretical foundation for analyzing Brownian particle dynamics.

Abstract

We develop a renormalized perturbation theory for the dynamics of interacting Brownian particles, which preserves the fluctuation-dissipation relation order by order. We then show that the resulting one-loop theory gives a closed equation for the density correlation function, which is identical with that in the standard mode coupling theory.