  We present a diagrammatic formulation of a theory for the time dependence of
density fluctuations in equilibrium systems of interacting Brownian particles.
To facilitate derivation of the diagrammatic expansion we introduce a basis
that consists of orthogonalized many-particle density fluctuations. We obtain
an exact hierarchy of equations of motion for time-dependent correlations of
orthogonalized density fluctuations. To simplify this hierarchy we neglect
contributions to the vertices from higher-order cluster expansion terms. An
iterative solution of the resulting equations can be represented by diagrams
with three and four-leg vertices. We analyze the structure of the diagrammatic
series for the time-dependent density correlation function and obtain a
diagrammatic interpretation of reducible and irreducible memory functions. The
one-loop self-consistent approximation for the latter function coincides with
mode-coupling approximation for Brownian systems that was derived previously
using a projection operator approach.
