BLOCH–NORDSIECK ESTIMATES OF A HIGH-TEMPERATURE SCALAR FIELD THEORY

Abstract

In anticipation of subsequent application to QED and QCD, we consider the case of a model, high temperature, relativistic, scalar field theory. We introduce into the exact, nonperturbative, functional expressions of this "quenched" model, a new Fradkin representation, and extract the infrared/Bloch–Nordsieck/(IR/BN) contributions of every perturbative graph, in order to circumvent the lack of a clear-cut 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. In momentum space, the former case displays a propagator which decays exponentially with increasing time, in addition to a new damping factor independent of time. The latter case displays an exponential growth with time of the symmetric pulse, generating effective and increasing plasmon waves, in competition with damping independent of time. When extended to QCD, qualitative applications could be made to RHIC scattering, in which a fireball appears, expands and is damped away.