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

We calculate the ground-state energy of a quark gas up to and including effecs of fourth order in the quark-gluon coupling. Renormalization-group techniques are used to rewrite the results of the fourth-order calculation in terms of a chemical-potential-dependent coupling. The chemical-potential-dependent coupling approaches zero at high densities. We argue that at hadronic matter densities a phase transition between quark matter and hadronic matter occurs. We show the existence of this phase transition for a three-color, one-flavor quark gas. We find a close correspondence between the results of quantum chromodynamics at large coupling with no bag constant and quantum chromodynamics at small coupling with a bag constant.