Chiral bag boundary conditions on the ball

TL;DR

This paper investigates chiral bag boundary conditions for massless spinor fields on Euclidean balls, showing that the zeta(0) value remains constant across a parameter range while heat-kernel coefficients depend on it.

Contribution

It proves the independence of the zeta(0) value from the boundary parameter theta for specific dimensions, revealing explicit theta-dependence of heat-kernel coefficients.

Findings

zeta(0) value is theta-independent in dimensions 2, 4, 6

heat-kernel coefficients depend on theta through hyperbolic functions

results apply to quantum cosmology and QCD bag models

Abstract

Local boundary conditions for spinor fields are expressed in terms of a 1-parameter family of boundary operators, and find applications ranging from (supersymmetric) quantum cosmology to the bag model in quantum chromodynamics. The present paper proves that, for massless spinor fields on the Euclidean ball in dimensions d=2,4,6, the resulting zeta(0) value is independent of such a theta parameter, while the various heat-kernel coefficients exhibit a theta-dependence which is eventually expressed in a simple way through hyperbolic functions and their integer powers.