Quantum Field Theory on Certain Non-Globally Hyperbolic Spacetimes

We study real linear scalar eld theory on two simple non-globally hyperbolic spacetimes containing closed timelike curves within the framework proposed by Kay for algebraic quantum eld theory on non-globally hyperbolic spacetimes. In this context, a spacetime (M; g) is said to be `F-quantum compatible' with a eld theory if it admits a -algebra of local observables for that theory which satis es a locality condition known as `F-locality'. Kay's proposal is that, in formulating algebraic quantum eld theory on (M; g), F-locality should be imposed as a necessary condition on the -algebra of observables. The spacetimes studied are the 2and 4-dimensional spacelike cylinders (Minkowski space quotiented by a timelike translation). Kay has shown that the 4dimensional spacelike cylinder is F-quantum compatible with massless elds. We prove that it is also F-quantum compatible with massive elds and prove the Fquantum compatibility of the 2-dimensional spacelike cylinder with both massive and massless elds. In each case, F-quantum compatibility is proved by constructing a suitable F-local algebra. PACS Numbers 04.62.+v E-mail address: [email protected] E-mail address: [email protected]