Christopher Fewster (York, England)
I describe how Bär's theory of Green hyperbolic partial differential operators can be generalized to nonlocal operators, where the nonlocality is confined to a compact spacetime region. Operators of this type arise in some models of the interaction between a field and a particle detector, but they can also be used to model "soft causality violation". It is shown that the nonlocal Green hyperbolic operators enjoy (suitable generalizations of) many of the properties of Green hyperbolic operators; in particular, they can be used as the starting point for a quantum field theory on curved spacetimes. If time permits, I will explain how this formalism permits a covariant description of the Unruh-deWitt particle detector model and indicates a new viewpoint on measurements in algebraic quantum field theory.
The talk describes work in progress with Rainer Verch (Leipzig).