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

Abstract

We calculate the ground-state energy of a relativistic electron gas up to and including effects of order ${\alpha }^{2}log\alpha$ and ${\alpha }^2$. 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 ${\alpha }^2$ are summed, are treated by performing a dimensional continuation to $4+\epsilon$ dimensions. Ultraviolet divergences associated with electron wave-function and charge renormalizations are rendered finite by use of a Landau gauge appropriate to $4+\epsilon$ dimensions. DOI: http://dx.doi.org/10.1103/PhysRevD.16.1147 © 1977 The American Physical Society