Spectral functions of the Dirac operator under local boundary conditions

TL;DR

This paper investigates the spectral properties of the Euclidean Dirac operator in two dimensions with local boundary conditions, focusing on the zeta and eta functions to understand spectral asymmetry and boundary effects.

Contribution

It provides a detailed analysis of the meromorphic structure of the zeta function and the boundary contribution to spectral asymmetry for the Dirac operator with local boundary conditions.

Findings

Meromorphic structure of the zeta function characterized

Boundary contribution to spectral asymmetry analyzed

Insights into spectral properties under local boundary conditions

Abstract

After a brief discussion of elliptic boundary problems and their properties, we concentrate on a particular example: the Euclidean Dirac operator in two dimensions, with its domain determined by local boundary conditions. We discuss the meromorphic structure of the zeta function of the associated second order problem, as well as the main characteristic of the first order problem, i.e., the boundary contribution to the spectral asymmetry, as defined through the eta function.