Effective action and density-functional theory

The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator functional of connected Green functions for the density and the photon field, offering systematic approximation schemes. The leading order of the perturbation expansion reproduces the Hartree-Fock equation. A renormalization-group motivated method is introduced to turn on the Coulomb interaction gradually and to find corrections to the Hartree-Fock and the Kohn-Sham schemes.