Nonlocal boundary conditions for massless spin-1/2 fields

Abstract

This paper studies the one-loop approximation for a massless spin-1/2 field on a flat four-dimensional Euclidean background bounded by two concentric three-spheres, when nonlocal boundary conditions of the spectral type are imposed. The use of $\ensuremath{\zeta}$-function regularization shows that the conformal anomaly vanishes, as in the case when the same field is subject to local boundary conditions involving projectors. The implications for one-loop properties of simple supergravity and Euclidean quantum gravity are briefly outlined.