Seminar

The Feynman propagator on Minkowski space is the inverse of the wave operator which is (at least formally) defined as a resolvent limit from the upper half-plane. Duistermaat and Hörmander gave a microlocal characterization valid in the general real-principal type case, and constructed a parametrix, but left open the question of existence of a canonical inverse. The Fredholm property was established only relatively recently by Gell-Redman, Haber and Vasy on classes of spacetimes including asymptotically Minkowski spaces, using radial propagation estimates. In this talk I will report on recent results on invertibility and related questions, and explain how to interpret the inverses in terms of global boundary conditions at infinity. Applications in Quantum Field Theory will be outlined. This is based on joint works with Christian Gérard and András Vasy.