Spin on the 4-ball

TL;DR

This paper calculates the functional determinant for massless spin-half fields on the Euclidean 4-ball, highlighting differences between spectral and mixed boundary conditions, and extends some results to higher spins.

Contribution

It provides the first detailed calculation of the functional determinant for spin-half fields on the 4-ball, comparing spectral and mixed boundary conditions, and discusses higher-spin cases.

Findings

The determinant differs for spectral and mixed boundary conditions.

The local boundary condition result aligns with conformal arguments.

Higher-spin results are also presented.

Abstract

Using known mode properties, the functional determinant for massless spin-half fields on the Euclidean 4-ball is calculated and shown to be different for spectral (nonlocal) and mixed (local) boundary conditions. The local result agrees with that from a conformal argument. Some higher-spin results are also given.