The Feynman propagator for the wave equation with an inverse square potential

Dean Baskin (TAMU, College Station)

Jul 10. 2023, 15:30 — 16:20

In this talk I will outline a construction of the Feynman propagator for the wave equation with an inverse square potential on Minkowski space.  The construction relies on a number of techniques in geometric microlocal analysis though I will only be able to describe a few of them.  To construct the Feynman propagator we construct appropriate (variable order) weighted Sobolev spaces encoding the Feynman property, then show that a rescaling of the operator is Fredholm on these spaces and invertible for a range of weights.  The Fredholm result relies on propagation estimates (proved via microlocal commutator methods) as well as special function analysis (to invert a normal operator at infinity).  Because the propagation estimates naturally take place on the level of H^1, we also construct an adapted large pseudodifferential calculus in order to shift the orders.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Organizer(s):
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)