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Statistical field theory for simple fluids: mean field and Gaussian approximations

We present an exact field theoretical representation of the statistical mechanics of simple classical liquids with short-range pairwise additive interactions. The action of the field theory is obtained by performing a Hubbard-Stratonovich transformation of the configurational Boltzmann factor. The mean field and Gaussian approximations of the theory are derived and applications to the liquid-vapour transition considered.