Second order photon loops at finite temperature and charge renormalization

TL;DR

This paper calculates second order photon loop corrections at finite temperature in QED, deriving a temperature-dependent renormalized coupling and analyzing electromagnetic properties of a medium relevant for early universe and laboratory plasmas.

Contribution

It provides explicit two-loop corrections to photon self-energy at finite temperature and a renormalized coupling expression valid around T   m, extending previous one-loop results.

Findings

Derived temperature-dependent renormalized coupling constant.

Calculated photon mass, Debye length, and plasma frequency up to second order.

Identified limitations of the renormalization scheme at high temperatures.

Abstract

We present two loop corrections to photon self energy at finite temperature in real time formalism. An expression for renormalized coupling constant has been derived in a form that is relevant for all temperature ranges of interest in QED, specifically for temperatures around T \sim m, where m is electron mass. Temperature dependence is mainly contributed by hot fermions at T \ge m. We use the calculations of vacuum polarization to determine the dynamically generated mass of photon, Debye screening length, plasma frequency up to the second order in \alpha as well as the electromagnetic properties of a medium at m \le T \le 2m temperature. For higher temperatures, the existing renormalization scheme does not work well because of the increase in coupling constant. To exactly determine the validity of renormalization scheme, higher order calculations are required. The temperature T \sim m is of specific interest from the point of view of the early universe. Such calculations have acquired more significance recently due to the possibility of producing electron-positron plasmas in laboratory.