Gauge invariant derivative expansion of the effective action at finite temperature and density and the scalar field in 2+1 dimensions

TL;DR

This paper introduces a gauge-invariant derivative expansion method for calculating the one-loop effective action at finite temperature and density, applicable to complex background fields in 2+1 dimensions.

Contribution

It presents a novel derivative expansion technique that maintains gauge invariance without simplifying assumptions, applicable to arbitrary background configurations in finite temperature and density settings.

Findings

Effective action computed up to second order in derivatives.

Method preserves gauge invariance under all transformations.

Application to scalar fields in 2+1 dimensions demonstrated.

Abstract

A method is presented for the computation of the one-loop effective action at finite temperature and density. The method is based on an expansion in the number of spatial covariant derivatives. It applies to general background field configurations with arbitrary internal symmetry group and space-time dependence. Full invariance under small and large gauge transformations is preserved without assuming stationary or Abelian fields nor fixing the gauge. The method is applied to the computation of the effective action of spin zero particles in 2+1 dimensions at finite temperature and density and in presence of background gauge fields. The calculation is carried out through second order in the number of spatial covariant derivatives. Some limiting cases are worked out.