2-COMPONENT SPINOR FIELDS IN TIME-NONORIENTABLE SPACETIMES

This paper examines spinor structures and two-component spinor fields in in a class of spacetimes that are space-orientable but not time-ori entable. The space-oriented frames form a principal bundle acted on by the group of proper nonorthochronous Lorentz transformations. This gr oup has two double coverings, Sin(+) and Sin(-), but only Sin(-) acts on the usual two-component spinors associated with Weyl neutrinos in M inkowski space. Consideration is initially restricted to Lorentzian un iverses-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, bu t only a subclass has a Sin(-) structure. Inequivalent Sin(+)- and Sin (-)-spinor structures correspond to members of two classes of homomorp hisms from pi(l)((M) over bar) to Z(2), where (M) over bar is the orie ntable double covering of the spacetime manifold M. For general time-n onorientable spacetimes, a similar classification is obtained of Sin(/-) structures in terms of homomorphisms from pi(l)(E) to Z(2) where E is the bundle of space-oriented frames of M.