Dirac Operator on a disk with global boundary conditions

TL;DR

This paper calculates the functional determinant of a Dirac operator with an Abelian gauge field on a disk, applying Atiyah-Patodi-Singer boundary conditions, and explores its relation to the index theorem.

Contribution

It provides a novel computation of the Dirac operator's determinant on a disk with global boundary conditions, linking it to topological index theory.

Findings

Explicit formula for the functional determinant under specified boundary conditions

Connection established between the determinant and the Atiyah-Patodi-Singer index theorem

Insights into boundary effects on Dirac operators in two dimensions

Abstract

We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the connection between our result and the index theorem.