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The Feynman propagator and its positivity properties

  • Andras Vasy (Stanford University)
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Abstract

One usually considers wave equations as evolution equations, i.e. imposes initial data and solves them. Equivalently, one can consider the forward and backward solution operators for the wave equation; these solve an equation $Lu=f$, for say $f$ compactly supported, by demanding that $u$ is supported at points which are reachable by forward, respectively backward, time-like or light-like curves. This property corresponds to causality. But it has been known for a long time that in certain settings, such as Minkowski space, there are other ways of solving wave equations, namely 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 positivity properties, and the connection to spectral and scattering theory in Riemannian settings, self-adjointness, as well as to the classical parametrix construction of Duistermaat and Hormander.

seminar
7/9/20 3/9/23

Webinar Analysis, Quantum Fields & Probability

MPI for Mathematics in the Sciences Live Stream

Jochen Zahn

Leipzig University Contact via Mail

Roland Bauerschmidt

University of Cambridge

Stefan Hollands

Leipzig University & MPI MiS Leipzig

Christoph Kopper

Ecole Polytechnique Paris

Antti Kupiainen

University of Helsinki

Felix Otto

MPI for Mathematics in the Sciences Contact via Mail

Manfred Salmhofer

Heidelberg University