Two-component spinor fields in time-nonorientable spacetimes

Abstract

This paper examines spinor structures and two-component spinor fields in in a class of spacetimes that are space-orientable but not time-orientable. The space-oriented frames form a principal bundle acted on by the group of proper nonorthochronous Lorentz transformations. This group has two double coverings, Sin and Sin, but only Sin acts on the usual two-component spinors associated with Weyl neutrinos in Minkowski space. Consideration is initially restricted to Lorentzian universes-from-nothing, geometries, like antipodally identified deSitter space, that have a single spacelike boundary and a smooth metric with Lorentzian signature. Every such spacetime has a Sin structure, but only a subclass has a Sin structure. Inequivalent Sin- and Sin-spinor structures correspond to members of two classes of homomorphisms from to , where is the orientable double covering of the spacetime manifold M. For general time-nonorientable spacetimes, a similar classification is obtained of Sin structures in terms of homomorphisms from to where E is the bundle of space-oriented frames of M.