A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics (QCD). By means of the generating functional method, we prove that the quark propagator actually depends on p 4 + iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain μ when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain μ the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.