Balanced geometric Weyl quantization with applications to QFT on curved spacetimes.

Nom de l'orateur
Jan Derezinski
Etablissement de l'orateur
Katedra Metod Matematycznych Fizyki, Wydzial Fizyki, Uniwersytet Warszawski (Department of Mathematical Physics, Faculty of Physics, Warsaw University)
Date et heure de l'exposé
Lieu de l'exposé
Salle des seminaires

First I will describe a new pseudodifferential calculus for (pseudo-)Riemannian spaces, which in our opinion (my, D.Siemssen's and A.Latosiński's) is the most appropriate way to study operators on such a manifold. I will briefly describe its applications to computations of the asymptotics the heat kernel and Green's operator on RIemannian manifolds. Then I will discuss analogous applications to Lorentzian manifolds, relevant for QFT on curved spaces. I will mention an intriguing question of the self-adjointness of the Klein-Gordon operator. I will describe the construction of the (distinguished) Feynman propagator on asymptotically static spacetimes. I will show how our pseudodifferential calculus can be used to compute the full asymptotics around the diagonal of various inverses and bisolutions of the Klein-Gordon operator.