LORENTZIAN UNIVERSES FROM NOTHING

Lorentzian universes from nothing, are spacetimes with a single spacel ike boundary that nevertheless have smooth Lorentzian metrics. They ar e the Lorentzian counterpart of spacetimes with no past boundary that appear in the Hartle-Hawking prescription for a wavefunction of the un iverse. One can always choose metrics for which these Lorentzian space times have no closed timelike curves; time nonorientability is then th eir only causal pathology. Classically, such spacetimes are locally in distinguishable from their globally hyperbolic covering spaces, and th e initial-value problem for classical fields is globally well defined. However, the construction of a quantum field theory (QFT) is more pro blematic. One can define a family of local algebras on an atlas of glo bally hyperbolic subspacetimes. But one cannot extend a generic positi ve linear function from a single algebra to the collection of all loca l algebras without violating positivity. The difficulty can be overcom e by restricting the size of neighbourhoods so that the union of any p air is time orientable. The structure of local algebras and states is then locally indistinguishable from that of QFT on a globally hyperbol ic spacetime. But the theory allows too little information to fix the global evolution of a state, because correlations between held operato rs at a pair of points are defined only if a curve joining the points lies in a single neighbourhood. One could hope that the difficulties a re restrictions on the observables in a generalized sum-over-histories approach, but the conjecture remains unexplored.