Statistical field theory for simple fluids: The collective variables representation

An alternative representation of an exact statistical field theory for simple fluids, based on the method of collective variables, is presented. The results obtained are examined from the point of another version of theory that was developed recently by performing a Hubbard–Stratonovich transformation of the configurational Boltzmann factor [J.-M. Caillol, Mol. Phys. 101 (2003) 1617]. The analytical expressions for the pressure and the free energy are derived in two-loop approximation for both versions of theory and it is shown that they are indeed equivalent. The results yield a new type approximation within an untested approximation scheme.