Remarks on the Coulomb and covariant gauges in finite temperature QED

We compare the use of the Coulomb gauge in finite temperature QED with a recently proposed prescription for covariant gauges, in which only the transverse photon degrees of freedom are thermalized. Using the Landau rule as a guide, we clarify the relation between the retarded electron self-energy and the elements of the self-energy matrix in the real-time formulation of Finite Temperature Field Theory. The general results are illustrated by means of the one-loop expressions for the electron self-energy in a QED plasma.