Heat-kernel coefficients and functional determinants for higher-spin fields on the ball

TL;DR

This paper computes heat-kernel coefficients and functional determinants for higher-spin fields on a 4-dimensional ball, revealing differences in fermionic determinants under different boundary conditions.

Contribution

It provides explicit formulas for heat-kernel coefficients and determinants for higher-spin fields, including distinctions between boundary condition types.

Findings

Explicit heat-kernel coefficients for higher-spin fields

Calculated zeta functional determinants on the 4-ball

Identified differences in fermionic determinants based on boundary conditions

Abstract

The zeta function associated with higher-spin fields on the Euclidean $4$-ball is investigated. The leading coefficients of the corresponding heat-kernel expansion are given explicitly and the zeta functional determinant is calculated. For fermionic fields the determinant is shown to differ for local and spectral boundary conditions.