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Chiral Bag Boundary Conditions on the Ball
Giampiero Esposito and Klaus Kirsten
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.