Vanishing magnetic mass in QED$_{3}$ with a Chern-Simons term

TL;DR

This paper proves that the magnetic mass in QED, including QED$_{3}$ with a Chern-Simons term, vanishes at finite temperature to all orders, supported by explicit two-loop calculations and a general proof.

Contribution

It provides a general proof that the magnetic mass vanishes at finite temperature in QED in any dimension, extending previous one- and two-loop results.

Findings

Magnetic mass vanishes at one loop in QED at finite temperature.

Two-loop calculations confirm the magnetic mass remains zero in QED$_{3}$ with a Chern-Simons term.

A simple proof shows the magnetic mass vanishes to all orders in this theory.

Abstract

We show that, at one loop, the magnetic mass vanishes at finite temperature in QED in any dimension. In QED$_{3}$, even the zero temperature part can be regularized to zero. We calculate the two loop contributions to the magnetic mass in QED$_{3}$ with a Chern-Simons term and show that it vanishes. We give a simple proof which shows that the magnetic mass vanishes to all orders at finite temperature in this theory. This proof also holds for QED in any dimension.