Field theoretical representation of the Hohenberg-Kohn free energy for fluids

To go beyond Gaussian approximation to the Hohenberg-Kohn free energy playing the key role in the density functional theory (DFT), the density functional integral representation would be relevant, because the field theoretic approach to perturbative calculations becomes available. Then we first derive the associated Hamiltonian of the density functional, explicitly including the logarithmic entropy term, from the grand partition function expressed by configurational integrals. Moreover, two things are done so that the efficiency of the obtained form may be revealed: we demonstrate that this representation facilitates the field theoretic treatment of the perturbative calculation and, further, compare our perturbative formulation with that of the DFT.