QUANTUM-FIELD THEORY ON CERTAIN NON-GLOBALLY HYPERBOLIC SPACETIMES

We study real linear scalar field theory on two simple non-globally hy perbolic spacetimes containing closed timelike curves within the frame work proposed by Kay for algebraic quantum field theory on non-globall y hyperbolic spacetimes. In this context, a spacetime (M, g) is said t o be 'F-quantum compatible' with a field theory if it admits a -algeb ra of local observables for that theory which satisfies a locality con dition known as 'F-locality'. Kay's proposal is that, in formulating a lgebraic quantum field theory on (M, g), F-locality should be imposed as a necessary condition on the -algebra of observables. The spacetim es studied are the two- and four-dimensional spacelike cylinders (Mink owski space quotiented by a timelike translation). Kay has shown that the four-dimensional spacelike cylinder is F-quantum compatible with m assless fields. We prove that it is also F-quantum compatible with mas sive fields and prove the F-quantum compatibility of the two-dimension al spacelike cylinder with both massive and massless fields. In each c ase, F-quantum compatibility is proved by constructing a suitable F-lo cal algebra.