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 $\mathit{\text{integral}}$ representation would be relevant, because field theoretical approach to perturbative calculations becomes available. Then the present letter first derives the associated Hamiltonian of density functional, explicitly including 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: to demonstrate that this representation facilitates the field theoretical treatment of the perturbative calculation, and further to compare our perturbative formulation with that of the DFT.