Quantum field theory in Lorentzian universes-from-nothing

We examine quantum field theory in spacetimes that are time nonorientable but have no other causal pathology. These are Lorentzian universesfrom -nothing, spacetimes with a single spacelike boundary that nevertheless have a smooth Lorentzian metric. A time-nonorientable, spacelike hypersurface serves as a generalized Cauchy surface, a surface on which freely specified initial data for wave equations have unique global time evolutions. A simple example is antipodally identified deSitter space. Classically, such spacetimes are locally indistinguishable from their globally hyperbolic covering spaces. The construction of a quantum field theory is more problematic. Time nonorientability precludes the existence of a global algebra of observables, and hence of global states, regarded as positive linear functions on a global algebra. One can, however, define a family of local algebras on an atlas of glob1 ally hyperbolic subspacetimes, with overlap conditions on the intersections of neighborho..