Calculation of equation of state of QCD at finite chemical potential and temperature

In this paper, using path integral techniques we derive a model-independent formula for the pressure density P(mu, T) (or equivalently the partition function) of Quantum Chromodynamics (QCD), which gives the equation of state (EOS) of QCD at finite chemical potential and temperature. In this formula the pressure density P(mu, T) consists of two terms: the first term P(mu, T)vertical bar(T=0)) is a p-independent (but T-dependent) constant; the second term is totally determined by G[mu, T]((p) over right arrow, omega(n)) (the dressed quark propagator at finite mu and finite T), which contains all the nontrivial mu-dependence. Then, in the framework of the rainbow-ladder approximation of the Dyson-Schwinger (DS) approach and under the approximation of neglecting the mu-dependence of the dressed gluon propagator, we show that G[mu, T] ((p) over right arrow, omega(n)) can be obtained from G[T] ((p) over right arrow, omega(n)) (the dressed quark propagator at mu = 0) by the substitution omega(n) -> omega(n) + i mu. This result facilitates numerical calculations considerably. By this result, once G [T] ((p) over right arrow, omega(n)) is known, one can determine the EOS of QCD under the above approximations (up to the additive term Y (,u, T) I T=O). Finally, a comparison of the present EOS of QCD and the EOS obtained in the previous literatures in the framework of the rainbow-ladder approximation of the DS approach is given. It is found that the EOS given in the previous literatures does not satisfy the thermodynamic relation P(mu, T) = a P(mu, T)/partial derivative mu vertical bar T.