A0--condensation in quark-gluon plasma with finite baryon density

Abstract

In the present paper, we return to the problem on a spontaneous generation of the $A_0$-background field in QCD at finite temperature and include in addition a quark chemical potential, $\mu$. We reproduce the known expressions in terms of Bernoulli's polynomials for the gluons and quarks using the same formalism. Then we calculate the $\mu$-dependence, both for small $\mu$ as expansion, and numerically for finite $\mu$. One result is that the chemical potential only weakly changes the values of the condensed field, but quite strongly deepens the minima of the effective potential. The gauge dependence of the condensation is discussed in terms of Nielsen's identity. It also is expressed in terms of Polyakov's loop. Both these representations guarantee gauge invariance of the condensation phenomenon. Also, we discuss the dependence of the Polyakov loop in the minimum of the effective potential on the chemical potential.