AG Mathematische Physik, Onirban Islam (Potsdam): Feynman propagators on curved spacetimes

Onirban Islam (Potsdam)

Feynman propagators on curved spacetimes

Abstract: It is a classic result that any wave operator on a globally hyperbolic
spacetime admits unique advanced and retarded propagators. With the advent of
quantum field theory, a new type of propagator emerges—the Feynman propagator.
These propagators are an essential ingredient of quantum field theory and are
intimately connected with quantum states. Moreover, they arise naturally in
global and spectral analyses on Lorentzian manifolds. In contrast to the
advanced and retarded propagators, Feynman propagators are not unique unless the
spacetime admits time-translation symmetry. In this talk, I shall present a
construction of Feynman propagators satisfying a positivity property based on
the idea of microlocalisation which, in a sense, is a tool to connect a
first-order pseudodifferential operator to the partial derivative. This, in
turn, provides a new construction of Hadamard states. I shall first introduce
the required notions from microlocal analysis and then explain microlocalisation
in a geometric fashion. (Joint work with Alexander Strohmaier based on
arXiv:2012.09767 [math.AP])