Quantum Fields in Curved Spacetime :

We brieey review the current status of the algebraic approach to quantum eld theory on globally hyperbolic spacetimes, both axiomatic { for general eld 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. and explain how it can be formulated at an axiomatic level for a general eld theory (as a condition on algebras-with-net-structure) on both globally hyperbolic and non globally hyperbolic space-times. 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.