(2+1)-Dimensional Fermion Determinant in a Constant Background Field at Finite Temperature and Density

TL;DR

This paper provides an exact evaluation of the fermion determinant in 2+1 dimensions under constant background fields at finite temperature and density, revealing non-extensive effects in the effective action.

Contribution

It offers a novel exact calculation of the fermion determinant in 2+1 dimensions considering finite temperature and chemical potential, including non-relativistic and relativistic cases.

Findings

Exact fermion determinant expressions derived

Demonstrates non-extensive behavior in the effective action

Decouples systems into 1+1 fermions via Fourier transformation

Abstract

We evaluate exactly both the non-relativistic and relativistic fermion determinant in 2+1 dimensions in a constant background field at finite temperature. The effect of finite chemical potential is also considered. In both cases, the systems are decoupled into an infinite number of 1+1 fermions by Fourier transformation in the $\beta$-variable. The total effective actions demonstrate non-extensiveness in the $\beta$ dimension.