Coulomb screening in the two-time Keldysh-Green-function formalism

The correct formation of the two-time self-consistent Coulomb quantum kinetics with screening requires a polarization loop obeying the Ward identity stemming from the charge conservation. Otherwise an infrared divergence occurs. For a self-consistent self-energy without vertex part, a polarization loop which includes a vertex part calculated in the ladder approximation, is shown to satisfy the required Ward identity.