  More than half of a century has passed since the free energy of classical
fluids defined by second Legendre transform was derived as a functional of
density-density correlation function. It is now becoming an increasingly
significant issue to develop the correlation functional theory that encompasses
the liquid state theory, especially for glassy systems where out of equilibrium
correlation fields are to be investigated. Here we have formulated a field
theoretic perturbation theory that incorporates two-body fields (both of
density-density correlation field and its dual field playing the role of
two-body interaction potential) into a density functional integral
representation of the Helmholtz free energy. Quadratic density fluctuations are
only considered in the saddle-point approximation of two-body fields as well as
density field. We have obtained a set of self-consistent field equations with
respect to these fields, which simply reads a modified mean-field equation of
density field where the bare interaction potential in the thermal energy unit
is replaced by minus the direct correlation function given in the mean
spherical approximation. Such replacement of the interaction potential in the
mean-field equation belongs to the same category as the local molecular field
theory proposed by Weeks and co-workers. Notably, it has been shown that even
the mean-field part of the free energy functional given by the self-consistent
field theory includes information on short-range correlations between fluid
particles, similarly to the formulation of the local molecular field theory.
The advantage of our field theoretic approach is not only that the modified
mean-field equation can be improved systematically, but also that fluctuations
of two-body fields in nonuniform fluids may be considered, which would be
relevant especially for glass-forming liquids.
