Analytic behavior of the QED polarizability function at finite temperature

TL;DR

This paper analyzes how finite temperature affects the analytical properties of the QED polarizability function in an electron gas, revealing that non-analyticity persists and influences Friedel oscillations in the potential.

Contribution

It demonstrates that finite temperature causes the polarizability to become non-analytical, maintaining Friedel oscillations, unlike the zero temperature case.

Findings

Polarizability is non-analytical at finite temperature.

Friedel oscillations survive at finite temperature.

Large-distance potential is related to polarizability's non-analytical properties.

Abstract

We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is not analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.