DEPARTMENT OF PHYSICS DISSERTATION DEFENSE: Mikhail Molodyk

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Title:  Distinguished propagators and states for quantum fields in asymptotically flat spacetimes

Abstract:  I will talk about several mathematical problems concerning quantum field theory in a broad class of asymptotically flat spacetimes with no symmetry assumptions, including radiative perturbations of Minkowski spacetime. I will use tools from microlocal analysis to define, in this generality, a distinguished in-out Feynman propagator and in-/out- asymptotic vacuum states for massive Klein-Gordon fields and discuss their properties, including a Lorentzian-signature version of the limiting absorption principle (the "i-epsilon prescription" for the Feynman propagator) and the Hadamard property of the vacuum states. These results provide a mathematically rigorous framework in which to study scattering of massive scalar quantum fields in asymptotically flat spacetimes, one which does not rely on explicit mode decompositions or asymptotic expansions for classical waves.