Spectral invariants for the Dirac equation on the d-Ball with various boundary conditions

TL;DR

This paper investigates spectral properties and boundary conditions for massless spin-half fields on a d-dimensional ball, deriving functional determinants and heat-kernel coefficients as polynomials in dimension.

Contribution

It provides new explicit calculations of spectral invariants and heat-kernel coefficients for the Dirac equation with various boundary conditions on the d-ball.

Findings

Derived spectral and mode properties for different boundary conditions.

Calculated functional determinants for the Dirac operator.

Expressed heat-kernel coefficients as polynomials in dimension d.

Abstract

The mode properties for spectral and mixed boundary conditions for massless spin-half fields are derived for the $d$--ball. The corresponding functional determinants and heat-kernel coefficients are presented, the latter as polynomials in $d$.