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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.
Item Metadata
Title |
Feynman Propagators and the Self-Adjointness of the Kleinâ Gordon Operator
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-07-30T10:05
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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. |
Extent |
22.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Wuppertal
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Series | |
Date Available |
2019-03-14
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0376879
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International