Speaker: Michal Wrochna (Stanford University)

Title: Scattering theory approach to the Feynman problem for the wave equation

Abstract: A classical result of Duistermaat and Hörmander provides four parametrices for the wave equation, distinguished by their wave front set. In applications in Quantum Field Theory one is interested in constructing the corresponding exact inverses, satisfying in addition a positivity condition. I will present a method (derived in a joint work with C. Gérard and dating back to W. Junker), where this is achieved by diagonalizing the wave equation in terms of elliptic pseudodifferential operators and solving the Cauchy problem with possible smooth remainders. I will then indicate possible ways of replacing Cauchy data by scattering data and comment on how this relates to global constructions of Feynman propagators.