Abstract
We attempt to prove the existence of Reeh-Schlieder states on curved spacetimes in the framework of locally covariant quantum field theory using the idea of spacetime deformation and assuming the existence of a Reeh-Schlieder state on a diffeomorphic (but not isometric) spacetime. We find that physically interesting states with a weak form of the Reeh-Schlieder property always exist and indicate their usefulness. Algebraic states satisfying the full Reeh-Schlieder property also exist, but are not guaranteed to be of physical interest.
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Acknowledgement
I would like to thank Chris Fewster for suggesting the current approach to the Reeh-Schlieder property and for many helpful discussions and comments on the second draft. Many thanks also to Lutz Osterbrink for his careful proofreading of the first draft. Finally I would like to express my gratitude to the anonymous referee for pointing out some minor mistakes and providing useful comments.
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Communicated by G. W. Gibbons
Dedicated to Klaas Landsman, out of gratitude for the support he offered when it was most needed
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Sanders, K. On the Reeh-Schlieder Property in Curved Spacetime. Commun. Math. Phys. 288, 271–285 (2009). https://doi.org/10.1007/s00220-009-0734-3
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DOI: https://doi.org/10.1007/s00220-009-0734-3