Fermions and gauge vector mesons at finite temperature and density. II. The ground-state energy of a relativistic electron gas

We calculate the ground-state energy of a relativistic electron gas up to and including effects of order α²logα and α². Cutting rules are developed which relate a vacuum-graph expansion for the thermodynamic potential to phase-space integrals over Feynman amplitudes. Overlapping infrared divergences, which cancel when all contributions of order α² are summed, are treated by performing a dimensional continuation to 4+ε dimensions. Ultraviolet divergences associated with electron wave-function and charge renormalizations are rendered finite by use of a Landau gauge appropriate to 4+ε dimensions.