In anticipation of a subsequent application to QCD, we consider the case of QED at high temperature. We introduce a Fradkin representation into the exact, Schwingerian, functional expression of a fermion propagator, as well as a new and relevant version of the Bloch-Nordsieck model, which extracts the soft contributions of every perturbative graph, in contradistinction to the assumed separation of energy scales of previous semiperturbative treatments. Our results are applicable to the absorption of a fast particle which enters a heat bath, as well as to the propagation of a symmetric pulse within the thermal medium due to the appearance of an instantaneous, shockwave-like source acting in the medium. An exponentially decreasing time dependence of the incident particle’s initial momentum combines with a stronger decrease in the particle’s energy, estimated by a sum over all Matsubara frequencies, to model an initial “fireball,” which subsequently decays in a Gaussian fashion. When extended to QCD, qualitative applications could be made to RHIC scattering, in which a fireball appears, expands, and is damped away.

• Received 15 March 2008

DOI:https://doi.org/10.1103/PhysRevD.77.105027