Collective Excitations in Thermal QED_{3+1}: Survival of the Fittest

TL;DR

This paper investigates the spectrum of collective fermionic excitations in finite temperature QED_{3+1}, revealing that most additional modes are damped and only one propagates at high temperatures, ensuring the theory's consistency.

Contribution

It demonstrates that, despite multiple solutions in the perturbative spectrum, only one mode remains physically relevant at high temperature, confirming the absence of pathologies in thermal QED_{3+1}.

Findings

Four new solutions in the perturbative spectrum at finite temperature.

Only one mode propagates at temperatures above 10M.

Other modes are strongly damped and nonphysical residues are present.

Abstract

The spectrum of collective fermionic excitations in a finite temperature QED_{3+1} is studied in different regimes. It is shown that within the standard perturbation approach the one-loop dispersion equation, besides the ordinary one-particle excitation, has four new solutions. The additional excitations are gauge-dependent and two of them have nonphysical signs of residues in the propagator poles. The temperature evolution of the solutions is investigated and it is shown that the use of effective propagators leaves no more than one additional mode which becomes propagating at $T \bolpor 10M$, when the gauge invariance is restored. The other three modes, including those with nonphysical residues in the propagator poles, are always strongly damped, thus the thermal effects do not produce pathologies in QED_{3+1}.