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Feynman Propagators and the Self-Adjointness of the Kleinâ Gordon Operator Siemssen, Daniel

Description

The Feynman propagator is at the heart of quantum field theory. However, in quantum field theory in curved spacetimes, no locally covariant notion of a distinguished Feynman propagator exists.
Instead, often a distinguished class of Feynman propagators is considered, which share a common parametrix. Nevertheless, certain classes of spacetimes possess distinguished Feynman propagators.

First, I will give an in-depth introduction to propagators (Green functions) on curved spacetimes and their role in quantum field theory. In particular, I will highlight the importance of the so-called Hadamard states â an appropriate generalization of the Poincaré invariant vacuum state. Then, I will show that the free Kleinâ Gordon field on asymptotically static spacetimes comes equipped with a natural Feynman propagator (albeit globally constructed and generally not related to a state). Finally, I will argue that this Feynman propagator is closely related to the question of the self-adjointness of the Kleinâ Gordon operator on $L^2$(spacetime) and the boundary value of its resolvent.

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