Anomaly and Thermodynamics for 2D Spinors in the Aharonov--Bohm Gauge Field

TL;DR

This paper investigates the axial anomaly for 2D Euclidean Dirac fermions in the Aharonov--Bohm gauge, exploring how self-adjoint extensions influence the anomaly and its implications for the thermodynamics of anyon gases.

Contribution

It analyzes the axial anomaly's dependence on self-adjoint extensions of the Dirac operator in 2D and discusses its relevance to the second virial coefficient of anyon gases.

Findings

Anomaly depends on self-adjoint extensions of the Dirac operator.

Relevance of anomaly to the thermodynamics of anyon gases.

Insights into the role of boundary conditions in quantum anomalies.

Abstract

The axial anomaly is computed for Euclidean Dirac fermions on the plane. The dependence upon the self-adjoint extensions of the Dirac operator is investigated and its relevance concerning the second virial coefficient of the anyon gas is discussed.