The induced Chern-Simons term at finite temperature

TL;DR

This paper demonstrates that a derivative expansion focusing on spatial derivatives effectively computes the finite temperature induced Chern-Simons term in (2+1)-dimensional fermion systems coupled to gauge fields, without special constraints.

Contribution

It introduces a straightforward method using spatial derivative expansion to calculate the finite temperature induced Chern-Simons term without assuming gauge field constraints.

Findings

Successful calculation of the induced Chern-Simons term at finite temperature.

Method applicable to non-stationary and non-Abelian gauge fields.

Simplifies the analysis of topological terms in finite temperature field theory.

Abstract

It is argued that the derivative expansion is a suitable method to deal with finite temperature field theory, if it is restricted to spatial derivatives only. Using this method, a simple and direct calculation is presented for the radiatively induced Chern-Simons--like piece of the effective action of (2+1)-dimensional fermions at finite temperature coupled to external gauge fields. The gauge fields are not assumed to be subjected to special constraints, and in particular, they are not required to be stationary nor Abelian.