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Quantum Fields in Curved Spacetime: Non Global Hyperbolicity and Locality

Bernard S. Kay
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Abstract

We briefly review the current status of the algebraic approach to quantum field theory on globally hyperbolic spacetimes, both axiomatic -- for general field theories, and constructive -- for a linear Klein-Gordon model. We recall the concept of F-locality, introduced in the latter context in BS Kay: Rev. Math. Phys., Special Issue, 167-195 (1992) and explain how it can be formulated at an axiomatic level for a general field theory (as a condition on algebras-with-net-structure) on both globally hyperbolic and non globally hyperbolic spacetimes. We also discuss the current status of the question whether/when algebras satisfying F-locality can exist for the Klein-Gordon model on spacetimes which are chronology violating.

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Bernard S. Kay. 1997-04-27. Quantum Fields in Curved Spacetime: Non Global Hyperbolicity and Locality. https://arxiv.org/abs/gr-qc/9704075

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