2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196129Using 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.13 pages, 4 figures. Revised version (minor changes) accepted for publication in Phys. Rev. DHigh Energy Physics - TheoryHigh Energy Physics - Phenomenologytext