Calculation of Equation of State of QCD at Finite Chemical Potential and Temperature

Abstract

In this paper, using path integral techniques we derive a model-independent formula for the pressure density \U0001d4ab(μ,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 \U0001d4ab(μ,T) consists of two terms: the first term (\U0001d4ab(μ,T)|T=0) is a μ-independent (but T-dependent) constant; the second term is totally determined by G[μ,T](p⃗,ωn) (the dressed quark propagator at finite μ and finite T), which contains all the nontrivial μ-dependence. Then, in the framework of the rainbow-ladder approximation of the Dyson–Schwinger (DS) approach and under the approximation of neglecting the μ-dependence of the dressed gluon propagator, we show that G[μ,T](p⃗,ωn) can be obtained from G[T](p⃗,ωn) (the dressed quark propagator at μ = 0) by the substitution ωn → ωn + iμ. This result facilitates numerical calculations considerably. By this result, once G[T](p⃗,ωn) is known, one can determine the EOS of QCD under the above approximations (up to the additive term \U0001d4ab(μ,T)|T = 0). 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 .