  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.
