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The split property for locally covariant quantum field theories in curved spacetime

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JournalLetters in Mathematical Physics
DateE-pub ahead of print - 19 Sep 2015
DatePublished (current) - 2015
Issue number12
Volume105
Number of pages28
Pages (from-to)1633-1661
Early online date19/09/15
Original languageEnglish

Abstract

The split property expresses the way in which local regions of spacetime define subsystems of a quantum field theory. It is known to hold for general theories in Minkowski space under the hypothesis of nuclearity. Here, the split property is discussed for general locally covariant quantum field theories in arbitrary globally hyperbolic curved spacetimes, using a spacetime deformation argument to transport the split property from one spacetime to another. It is also shown how states obeying both the split and (partial) Reeh–Schlieder properties can be constructed, providing standard split inclusions of certain local von Neumann algebras. Sufficient conditions are given for the theory to admit such states in ultrastatic spacetimes, from which the general case follows. A number of consequences are described, including the existence of local generators for global gauge transformations, and the classification of certain local von Neumann algebras. Similar arguments are applied to the distal split property and circumstances are exhibited under which distal splitting implies the full split property.

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© Springer Science+Business Media Dordrecht 2015. This is an author produced version of a paper published in Letters in Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy.

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