Classical transport theory is employed to analyze the hot quark-gluon plasma at the leading order in the coupling constant. A condition on the (covariantly conserved) color current is obtained.From this condition, the generating functional of hard thermal loops with an arbitrary number of soft external bosonic legs can be derived. Our approach, besides being more direct than alternative ones, shows that hard thermal loops are essentially classical.
Classical transport theory for colored particles is investigated and employed to derive the hard thermal loops of QCD. A formal construction of phasespace for color degrees of freedom is presented. The gauge invariance of the non-Abelian Vlasov equations is veried and used as a guiding principle in our approximation scheme. We then derive the generating functional of hard thermal loops from a constraint satised at leading-order by the color current.This derivation is more direct than alternative ones based on perturbative quantum eld theory, and shows that hard thermal eects in hot QCD are essentially classical.As an illustration, we analyze color polarization in the QCD plasma.
Abstract:We examine the calculation of the critical temperature T c for the restoration of a spontaneously broken symmetry. Motivated by a set of recently developed gauge dependence identities, we give a gauge and parameterization independent definition of this temperature in terms of the physical mass of the scalar particle as determined by the propagator pole. As an explicit illustration, we consider the Abelian Higgs model in the unitary gauge, where the usual definition of the critical temperature based upon the effective potential leads to an erroneous result. We show how the gauge invariant definition reproduces the correct result as found in the "renormalizable" parameterizations.
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