  This paper presents a unified method for formulating a field-theoretic
perturbation theory that encompasses the conventional liquid state theory.
First, the free-energy functional of instantaneous correlation field is
obtained from the functional-integral representation of the grand potential.
Next, we demonstrate that the instantaneous free-energy functional yields a
closure relation between the correlation functions in the mean-field
approximation. Notably, the obtained closure relation covers a variety of
approximate closures introduced in the liquid state theory.
