Chiral limit of the two-dimensional fermionic determinant in a general magnetic field

TL;DR

This paper analyzes the behavior of the fermionic determinant in 2D QED under a general magnetic field, highlighting the role of the chiral anomaly in the small mass limit and presenting new scattering results.

Contribution

It provides a detailed analysis of the chiral limit of the fermionic determinant and introduces novel findings on electron scattering in inhomogeneous magnetic fields.

Findings

Small mass limit governed by the chiral anomaly

New low-energy scattering results in 2+1 dimensions

Effective action characterized for general magnetic fields

Abstract

We consider the effective action for massive two-dimensional QED in flat Euclidean space-time in the background of a general square-integrable magnetic field with finite range. It is shown that its small mass limit is controlled by the chiral anomaly. New results for the low-energy scattering of electrons in 2+1 dimensions in static, inhomogenous magnetic fields are also presented.