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Quantum Field Theory on Certain Non-Globally Hyperbolic Spacetimes

C. J. Fewster·A. Higuchi
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Abstract

We study real linear scalar field theory on two simple non-globally hyperbolic spacetimes containing closed timelike curves within the framework proposed by Kay for algebraic quantum field theory on non-globally hyperbolic spacetimes. In this context, a spacetime (M,g) is said to be `F-quantum compatible' with a field theory if it admits a *-algebra of local observables for that theory which satisfies a locality condition known as `F-locality'. Kay's proposal is that, in formulating algebraic quantum field theory on $(M,g)$, F-locality should be imposed as a necessary condition on the *-algebra of observables. The spacetimes studied are the 2- and 4-dimensional spacelike cylinders (Minkowski space quotiented by a timelike translation). Kay has shown that the 4-dimensional spacelike cylinder is F-quantum compatible with massless fields. We prove that it is also F-quantum compatible with massive fields and prove the F-quantum compatibility of the 2-dimensional spacelike cylinder with both massive and massless fields. In each case, F-quantum compatibility is proved by constructing a suitable F-local algebra.

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C. J. Fewster, A. Higuchi. 1995-08-24. Quantum Field Theory on Certain Non-Globally Hyperbolic Spacetimes. https://doi.org/10.1088/0264-9381%2F13%2F1%2F006

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