Second Order Thermal Corrections to Electron Wavefunction

TL;DR

This paper calculates second order thermal corrections to the electron wavefunction at generalized temperatures, demonstrating renormalizability of QED and enabling particle process calculations in extremely hot environments like the early universe.

Contribution

It introduces a novel method for calculating second order thermal corrections to the electron wavefunction at generalized temperatures, including hot and cold limits.

Findings

Results include corrections at intermediate, high, and low temperatures.

Method ensures removal of hot singularities during integration.

Comparison with existing results validates the approach.

Abstract

Second order perturbative corrections to electron wavefunction are calculated here at generalized temperature, for the first time. This calculation is important to prove the renormalizeability of QED through order by order cancellation of singularities at higher order. This renormalized wavefunction could be used to calculate the particle processes in the extremely hot systems such as the very early universe and the stellar cores. We have to re-write the second order thermal correction to electron mass in a convenient way to be able to calculate the wavefunction renormalization constant. A procedure for integrations of hot loop momenta before the cold loop momenta integration is maintained throughout to be able to remove hot singularities in an appropriate way. Our results, not only includes the intermediate temperatures T m (where m is the electron mass), the limits of high temperature T>>m and low temperature T<<m are also retrievable. A comparison is also done with the existing results.