Condiciones de contorno globales para el operador de Dirac

TL;DR

This paper evaluates the functional determinant of Dirac operators on manifolds with boundary, focusing on global boundary conditions and their relation to the index theorem, with specific results on a 2D disk with gauge fields.

Contribution

It introduces a method to compute functional determinants for Dirac operators with Atiyah-Patodi-Singer boundary conditions on manifolds with boundary.

Findings

Functional determinants are computed explicitly for a 2D disk with gauge fields.

Ellipticity of boundary value problems is characterized via the Calderon projector.

The connection between the determinant and the index theorem is discussed.

Abstract

Functional determinants for Dirac operators on manifolds with boundary are considered. Ellipticity of boundary value problems is discussed in terms of the Calderon projector. The functional determinant for a Dirac operator on a bidimensional disk, in the presence of an Abelian gauge field, subject to global boundary conditions of the type introduced by Atiyah-Patodi-Singer, is evaluated. The relationship with the index theorem is also commented.