Fermions and gauge vector mesons at finite temperature and density. I. Formal techniques

Abstract

We construct the thermodynamic potential for quantum electrodynamics and quantum chromodynamics at finite temperature and density. We find the thermodynamic potential as a functional of the full propagators and vertices. This functional is stationary under variations of the full propagators and vertices by virtue of the Schwinger-Dyson equations, and may be interpreted as a classical action. We also discuss the renormalization of the propagators and vertices.