QLunch: Propagators on curved spacetimes and balanced geometric Weyl quantization

Abstract: Physicists studying quantum field theory use various functions called propagators  or 2-point functions. Mathematically, these functions  can be understood as distinguished inverses and bisolutions of the Klein Gordon equation. I will discuss how to define them in the context of curved spacetimes. I will mention the intriguing  problem of  self-adjointness of the Klein-Gordon operator on non-stationary spacetimes.

Leading singularities of the Feynman propagator play an important role in renormalization of quantum fields. 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 such operators. If time permits, I will discuss how the new quantization can be used to compute  asymptotics of various propagators on curved spacetimes.