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 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 µ while the odd point functions are odd functions of µ 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.

Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

“…These pioneering papers lead to a number of important physical insights and applications: lightlight scattering in QED [9], pair production from vacuum in the presence of an electric field [10][11][12] and vacuum birefringence [13], among others. The one-loop QED effective lagrangian at finite temperature and density has been investigated in magnetic field background [14][15][16][17], in electric field background [18,19], in general background fields for the case of 0 + 1 [20,21] and 1 + 1 dimensional massless QED [22,23] and is very relevant and closely related to many physical phenomena such as, for example, the Casimir effect. When evaluating the QED effective lagrangian at finite temperature, the time component of the momentum four vector, over which we integrate, takes on only discrete values for a fixed temperature, while when computing the Casimir energy, an analogous substitution takes place in a space component of the momentum vector for a fixed distance between the plates.…”