Anomalous Magnetic Moment of Electron in Chern-Simons QED

TL;DR

This paper computes the electron's anomalous magnetic moment in 2+1 dimensional Chern-Simons QED, revealing divergences without a Chern-Simons term and temperature-dependent corrections when the term is present.

Contribution

It provides the first detailed analysis of the anomalous magnetic moment in Chern-Simons QED at finite temperature, highlighting the importance of the Chern-Simons term for infrared finiteness.

Findings

Infrared divergence occurs when the Chern-Simons term vanishes.

Thermal correction in Maxwell-Chern-Simons theory behaves as (1/β) log(β M).

No thermal correction in pure Chern-Simons theory.

Abstract

We calculate the anomalous magnetic moment of the electron in the Chern-Simons theory in 2+1 dimensions with and without a Maxwell term, both at zero temperature as well as at finite temperature. In the case of the Maxwell-Chern-Simons (MCS) theory, we find that there is an infrared divergence, both at zero as well as at finite temperature, when the tree level Chern-Simons term vanishes, which suggests that a Chern-Simons term is essential in such theories. At high temperature, the thermal correction in the MCS theory behaves as $\frac{1}{\beta} \ln \beta M$, where $\beta$ denotes the inverse temperature and $M$, the Chern-Simons coefficient. On the other hand, we find no thermal correction to the anomalous magnetic moment in the pure Chern-Simons (CS) theory.