Determinants of Dirac operators with local boundary conditions

TL;DR

This paper derives explicit formulas for the determinants of Dirac operators with local boundary conditions on manifolds, linking them to Green functions and applying to disk geometries with bag-like conditions.

Contribution

It provides a new explicit formula relating Dirac operator determinants to Green functions for local boundary conditions, with applications to disk geometries.

Findings

Explicit formula for Dirac determinants with local boundary conditions

Relation between determinants and Green functions established

Application to bidimensional disk with bag-like boundary conditions

Abstract

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.