QCD COUPLING-CONSTANT AT FINITE-TEMPERATURE

We work out the method for evaluating the QCD coupling constant at fin ite temperature (T) by making use of the finite T renormalization grou p equation up to the one-loop order on the basis of the background fie ld method with the imaginary time formalism. The background field meth od, which maintains the explicit gauge invariance, provides notorious simplifications since one has to calculate only the renormalization co nstant of the background field gluon propagator. The results for the e volution of the QCD coupling constant at finite T reproduce partially the ones obtained in the literature. We discuss, in particular, the or igin of the discrepancies between different calculations, such as the choice of gauge, the break-down of Lorentz invariance, imaginary versu s real time formalism and the applicability of the Ward identities at finite T.