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 fields on noncommutative spacetimes and "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.
The talk describes work in progress with Rainer Verch (Leipzig).
This talk is part of series of talks affiliated with the virtual Mittag-Leffler workshop "Scattering, microlocal analysis and renormalization", organized by Claudio Dappiaggi, Jacob Schach Møller and Michal Wrochna. The full schedule can be found at: