Abstract
We develop a field theoretical treatment of a model of interacting Brownian particles. Wepay particular attention to the requirement of time reversal invariance and thefluctuation-dissipation relationship (FDR). The method used is a modified version of theauxiliary field method due originally to Andreanov, Biroli and Lefevre (2006 J. Stat. Mech.P07008). We recover the correct diffusion law when the interaction is dropped as well asthe standard mode coupling equation in the one-loop order calculation for interactingBrownian particle systems. It is noteworthy that despite our starting dynamical modelcontaining the bare inter-particle interaction potential, it cancels out and the directcorrelation function emerges in the end result due to our use of the correct staticinput.
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