Abstract
In this paper we propose a general method for calculating the partition function of QCD at finite chemical potential. It is found that the partition function is totally determined by the dressed quark propagator at finite chemical potential up to a multiplicative constant. From this a criterion for the phase transition between the Nambu and the Wigner phase is obtained. This general method are applied to two specific cases: the free quark theory and QCD with a model dressed quark propagator proposed in H . Pagels and S. Stokar, Phys. Rev. D20, 2947 (1979). In the first case, the standard Fermi distribution at T = 0 are reproduced. In the second case, a particular form of baryon number distribution is obtained. It is found that when μ is below a critical value, the baryon number density is identically zero, which agrees with the general conclusion in M. A. Halasz et al., Phys. Rev. D58, 096007 (1998). All the results in the present paper are obtained under the condition T = 0 and μ ≠ 0. However, they can be generalized to the the general situation T ≠ 0 and μ ≠ 0 without fundamental difficulty.
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