Exact Effective action for (1+1)-dimensional fermions in an Abelian background at finite temperature and chemical potential

TL;DR

This paper calculates the effective action for massless (1+1)-dimensional fermions in an abelian background at finite temperature and chemical potential, revealing how chemical potential influences amplitude structures without affecting the chiral anomaly.

Contribution

It provides an exact calculation of the effective action including chemical potential effects, extending previous zero chemical potential results and clarifying symmetry properties.

Findings

Odd point functions do not vanish at finite chemical potential.

Even point functions are even functions of chemical potential.

Chiral anomaly remains unaffected by chemical potential.

Abstract

In this paper we study the effects of a nonzero chemical potential in the effective action for massless fermions in (1+1) dimensions in an abelian gauge field background at finite temperature. We calculate the n-point function and show that the structure of the amplitudes corresponds to a generalization of the structure noted earlier in a calculation without a chemical potential (the associated integrals carry the dependence on the chemical potential). Our calculation shows that the chiral anomaly is unaffected by the presence of a chemical potential at finite temperature. However, unlike the earlier calculation (in the absence of a chemical potential) odd point functions do not vanish. We trace this to the fact that in the presence of a chemical potential the generalized charge conjugation symmetry of the theory allows for such amplitudes. In fact, we find that all the even point functions are even functions of the chemical potential while the odd point functions are odd functions of it which is consistent with this generalized charge conjugation symmetry. We show that the origin of the structure of the amplitudes is best seen from a formulation of the theory in terms of left and right handed spinors. The calculations are also much simpler in this formulation and it clarifies many other aspects of the theory.