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The heat kernel expansion for field theory at finite temperature isconstructed. It is based on the imaginary time formalism and applies to genericKlein-Gordon operators in flat space-time. Full gauge invariance is manifest ateach order of the expansion and the Polyakov loop plays an important role atany temperature. The expansion is explicitly worked out up to operators ofdimension six included. The method is then applied to compute the one loopeffective action of QCD at finite temperature with massless quarks. Thecalculation is carried out within the background field method in the$\bar{\text{MS}}$ scheme up to dimension six operators. Further, the action ofthe dimensionally reduced effective theory at high temperature is also computedto the same order. Existing calculations are reproduced and new results areobtained in the quark sector for which only partial results existed up todimension six.Comment: 28 pages RevTe

Thermal heat kernel expansion and the one-loop effective action of QCD at finite temperature