  Using the mixed space representation, we extend our earlier analysis to the
case of Dirac and gauge fields and show that in the absence of a chemical
potential, the finite temperature Feynman diagrams can be related to the
corresponding zero temperature graphs through a thermal operator. At non-zero
chemical potential we show explicitly in the case of the fermion self-energy
that such a factorization is violated because of the presence of a singular
contact term. Such a temperature dependent term which arises only at finite
density and has a quadratic mass singularity cannot be related, through a
regular thermal operator, to the fermion self-energy at zero temperature which
is infrared finite. Furthermore, we show that the thermal radiative corrections
at finite density have a screening effect for the chemical potential leading to
a finite renormalization of the potential.
