Quantum Field Theory on Certain Non-Globally Hyperbolic Spacetimes

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.

14 pages, latex, one figure (incorporated in latex source)

References in corpus (5)

• Quantum Field Theory in Spaces with Closed Time-Like Curves
• Simple Quantum Systems in Spacetimes with Closed Timelike Curves
• Unitarity Restoration in the Presence of Closed Timelike Curves
• Unitarity of Quantum Theory and Closed Time-Like Curves
• Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes

Cited by in corpus (5)

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• Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
• A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordström Black Hole
• Quantum fields on semi-globally hyperbolic space-times