Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
It is a classic result that any normally hyperbolic 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 perturbative quantum field theory and they are intimately connected with quantum states. They also play a pivotal role in Lorentzian generalisations of the index theorem and the Duistermaat-Guillemin-Gutzwiller trace formula, for instance. I shall talk about the existence and uniqueness of these propagators for wave-type and Dirac-type operators on a globally hyperbolic spacetime. In order to sketch the proof of the former, microlocalisation of a normally hyperbolic operator will be explained, whilst for the latter a more direct approach will be presented.