Feynman Propagators on Curved Spacetime

Explore a comprehensive lecture on Feynman propagators in curved spacetime, delivered as part of the Thematic Programme on "Spectral Theory and Mathematical Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the construction of Feynman propagators for normally hyperbolic operators, examining their unique properties and essential role in quantum field theory. Investigate the connection between Feynman propagators and quantum states, as well as their significance in global and spectral analyses on Lorentzian manifolds. Learn about the microlocalisation technique used to construct Feynman propagators with positivity properties, and discover a novel approach for Dirac-type operators. Gain insights into the microlocal construction of Hadamard states for wave and Dirac-type operators, based on joint work with A. Strohmaier (arXiv:2012.09767 [math.AP]).