BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andras Vasy (Stanford) DTSTART:20210701T150000Z DTEND:20210701T163000Z DTSTAMP:20260423T035911Z UID:AQFP/11 DESCRIPTION:Title: Th e Feynman propagator and its positivity properties\nby Andras Vasy (St anford) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstra ct\nOne usually considers wave equations as evolution equations\, i.e. imp oses initial data and solves them. Equivalently\, one can consider the for ward and backward solution operators for the wave equation\; these solve a n equation $Lu=f$\, for say $f$ compactly supported\, by demanding that $u $ is supported at points which are reachable by forward\, respectively bac kward\, time-like or light-like curves. This property corresponds to causa lity. But it has been known for a long time that in certain settings\, suc h as Minkowski space\, there are other ways of solving wave equations\, na mely the Feynman and anti-Feynman solution operators (propagators). I will explain a general setup in which all of these propagators are inverses of the wave operator on appropriate function spaces\, and also mention posit ivity properties\, and the connection to spectral and scattering theory in Riemannian settings\, self-adjointness\, as well as to the classical para metrix construction of Duistermaat and Hormander.\n LOCATION:https://researchseminars.org/talk/AQFP/11/ END:VEVENT END:VCALENDAR