Axial Anomaly in the Presence of the Aharonov-Bohm Gauge Field

TL;DR

This paper explores how the axial anomaly for Euclidean Dirac fermions on a plane is affected by an Aharonov-Bohm gauge potential, emphasizing the importance of self-adjoint extensions and local current definitions.

Contribution

It provides a non-perturbative analysis of the axial anomaly considering self-adjoint extensions and discusses the influence of quantum parameters and local current definitions.

Findings

The axial anomaly depends on the choice of self-adjoint extension.

Quantum mechanical parameters influence the anomaly expression.

Effective action derivation via stereographic projection is presented.

Abstract

We investigate on the plane the axial anomaly for euclidean Dirac fermions in the presence of a background Aharonov--Bohm gauge potential. The non perturbative analysis depends on the self--adjoint extensions of the Dirac operator and the result is shown to be influenced by the actual way of understanding the local axial current. The role of the quantum mechanical parameters involved in the expression for the axial anomaly is discussed. A derivation of the effective action by means of the stereographic projection is also considered.