  The equations of motion for the density modes of a fluid, derived from
Newton's equations, are written as a linear generalized Langevin equation. The
constraint imposed by the fluctuation-dissipation theorem is used to derive an
exact form for the memory function. The resulting equations, solved under the
assumption that the noise, and consequently density fluctuations, of the liquid
are gaussian distributed, are equivalent to the random-phase-approximation for
the static structure factor and to the well known ideal mode coupling theory
(MCT) equations for the dynamics. This finding suggests that MCT is the
canonical mean-field theory of the fluid dynamics.
