Exact Results in Quantum Theory

Quantum Field Theory on curved spacetimes is one of the most basic formalisms of theoretical physics. It might be expected that one cannot say anything new about its foundations. Surprisingly, it seems that some elements of its basic mathematical structure have been clarified only recently in my work with Daniel Siemssen.One of such elements is the notion of the (in-out) Feynman propagator. I will explain what it is in asymptotically stationary stable spacetimes. I will also discuss how the Feynman propagator is related to the essential self-adjointness of the Klein-Gordon operator.