Bloch-Nordsieck Estimates of High-Temperature QED

TL;DR

This paper develops a high-temperature QED model using a novel Bloch-Nordsieck approach, incorporating a Fradkin representation to better understand soft contributions and particle behavior in thermal media, with potential applications to QCD phenomena.

Contribution

It introduces a new Bloch-Nordsieck model and Fradkin representation for high-temperature QED, enabling detailed analysis of soft contributions and particle dynamics in thermal environments.

Findings

Model describes particle absorption and pulse propagation in heat bath.

Exponential decay of initial momentum and energy modeled by Matsubara frequencies.

Potential extension to QCD for RHIC scattering phenomena.

Abstract

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 (BN) model, which extracts the soft contributions of every perturbative graph, in contradistinction to the assumed separation of energy scales of previous semi-perturbative 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, shock-wave-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.