Free-energy functional of instantaneous correlation field in liquids: field-theoretic derivation of the closures

Abstract

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.