“Balanced Geometric Weyl Quantization with Applications to QFT on Curved Spacetimes

First I will describe a new pseudodifferential calculus for (pseudo-)Riemannian spaces, which in our opinion (my, D.Siemssen’s and A.LatosiĆski’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.

### Details

Geometry SeminarJan Derezinski (Warsaw)

August 15, 2018

3:15 PM - 4:15 PM

More information available at:

http://mathematics.stanford.edu/geometry-w/

### Location

Math 383-N450 Serra Mall

Bldg. 380

Room 383-N

Stanford CA 94305