Hamiltonian lattice QCD at finite temperature and chemical potential. II. Gauss-law constraint on the thermal excitations.

Abstract

We study the restoration of global symmetries of lattice QCD at finite temperature T and chemical potential \ensuremath{\mu}, studying in detail the consequences of local gauge invariance. The Hamiltonian of lattice SU(${N}_{c}$) QCD in the ${A}^{0}$=0 gauge has to be supplemented by the Gauss-law constraint. To introduce the temperature in a consistent way, thermal excitations must respect this condition. We examine this problem in the strong-coupling limit but at fixed ${N}_{c}$ and for one flavor. The free energy to be minimized (in a Bogoliubov approximation) must be defined by traces over states restricted to be local color singlets. To compute these traces one can make use of the orthogonality and linear independence relations of the characters of the SU(${N}_{c}$) gauge group. We first consider the simple case of SU(2) and then we generalize to SU(${N}_{c}$). We find that the critical curve in the T-\ensuremath{\mu} plane depends on ${N}_{c}$. The critical temperature ${T}_{c}$ (\ensuremath{\mu}=0) increases with ${N}_{c}$ (linearly for large ${N}_{c}$), but the critical chemical potential ${\ensuremath{\mu}}_{c}$ (T=0) remains constant ${\ensuremath{\mu}}_{c}$=${m}_{0}$, ${m}_{0}$ being the dynamical mass at T=\ensuremath{\mu}=0. The shape of the critical curve and the thermodynamic properties remain, however, similar to the ones computed with a free energy unconstrained by the Gauss law. The effect of the Gauss-law constraint has been to increase the critical temperature, as the effective number of degrees of freedom that can be thermally excited has decreased.