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

Abstract

In this paper we study the effects of a nonzero chemical potential in $(1+1)$-dimensional quantum field models at finite temperature. We particularly consider massless fermions in an Abelian gauge field background and calculate the effective action by evaluating the $n$-point functions. We find 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 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 $\ensuremath{\mu}$, while the odd point functions are odd functions of $\ensuremath{\mu}$ 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.