Abstract
The effective action and background field method have been applied to investigate free energy density for non-Abelian gauge theory at finite temperature, in which quantum corrections are included and certain symmetries of generating functional are restored. Renormalization is also considered for the gauge field. We give result for the one loop free energy density of gauge theory at high temperature and non-zero chemical potential, correcting a result previously at zero temperature and density. Some results are extended up to two loops
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