In this paper, we extend the study of bremsstrahlung photon production in a quark-gluon plasma to the cases of soft static photons and hard real photons. The general framework of this study is the effective perturbative expansion based on the resummation of hard thermal loops. Despite the fact that bremsstrahlung only comes at two loops, we find that in both cases it generates contributions of the same order of magnitude as those already calculated by several other groups at one loop. Furthermore, a new process contained in the two-loop diagrams dominate the emission of a very hard real photon. In all cases, the rate of real or virtual photon production in the plasma is appreciably increased compared to the one-loop predictions.Comment: 35 pages, LaTeX2e, uses class article and package graphics, 13 postscript figure

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We derive the Ward identities that determine the gauge dependence of the QCD dispersion relations obtained from the ordinary gluon propagator in a certain class of gauges. These identities hold for complex structure functions at both zero and finite temperature. A direct consequence of our analysis is that the gauge dependence of the gluon-plasma damping constant obtained in recent one-loop calculations is due to an inconsistent approximation scheme.PACS numbers: 12.38.Mh At high temperatures and pressures, hadronic matter is thought to undergo a phase transition to a deconfined plasma phase consisting of weakly interacting, deconfined quarks and gluons.' There has been a great deal of controversy in recent years, however, concerning the stability of this plasma against external perturbations.^'^ This controversy has been triggered in part by the gauge-fixing dependence of the gluon-plasma dispersion relations at the one-loop level. Although all oneloop calculations yield the same lowest-order plasma frequency for both the transverse gluon mode and the spatially longitudinal plasmon mode, the rate at which the plasma oscillations are damped seems to be gauge-fixing dependent, both with respect to magnitude and sign. Despite the fact that there exist arguments concerning the need to incorporate higher-loop corrections,"* much of the controversy has focused on the correct definition of dispersion relations in hot QCD. In particular, several groups^ have proposed dispersion relations derived from modified, manifestly gauge-fixing-independent gluon propagators. In these formulations gauge dependence of the propagator, and hence of the related dispersion relations, cancels algebraically order by order in the loop expansion. As well, calculations based on color-electric and -magnetic correlation functions have been motivated in part by the apparent gauge-fixing dependence of the damping constant.^ It is worth noting, however, that these modified approaches still do not agree on the value of the one-loop damping constant. Pisarski,"* on the other hand, has stated that the physical poles in the ordinary gluon propagator would be gauge independent if calculated accurately.The purpose of this Letter is to clarify the issues raised in the above controversy by deriving a set of generalized Ward identities that govern the gauge dependence, in a wide class of gauges, of the QCD propagator and hence of the QCD plasma dispersion relations. The derivatio. of the identities is nonperturbative and does not distinguish between zero and finite temperature nor between real and imaginary parts of the structure functions. Given certain additional assumptions that will be made explicit in the following, the identities imply the gaugefixing independence of the physical poles in the gluon propagator in the class of gauges considered here. At this level, our discussion simply generalizes earlier claims concerning gauge-fixing independence of the poles based on the S matrix'''^ or on renormalization-group arguments,^ neither of which are imm...