Jan Dereziński (University of Warsaw)

The Analysis and PDE seminar will take place Monday, Aug 27, in 740 Evans from 4-5pm.

Title: Balanced geometric Weyl quantization with applications to QFT on curved spacetimes

Abstract: 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.