Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime
type: Item
instance of: scholarly article
title: Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime
zbMATH Open document ID: 1113.81104
author: Claudio D'Antoni
author: Stefan Hollands
published in: Communications in Mathematical Physics
publication date: 2007-02-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/math-ph/0106028
review text: The authors present several structural properties for a free Dirac quantum field on a globally hyperbolic spacetime. They prove that any two quasifree Hadamard states on the algebra of free Dirac fields are locally quasiequivalent and, on a globally hyperbolic spacetime, the associated local von Neumann algebras are factors of type III\(_1\) which are locally unitarily equivalent. They verify that the theory of a free Dirac field on a static spacetime satisfies the nuclearity condition in the sense of Buchholz and Wichmann. Using this result they prove that on a globally hyperbolic spacetime, the split-property holds in the representation of any quasifree Hadamard state.
reviewed by: Lajos Molnár
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 46N50
zbMATH DE Number: 5125427
zbMATH Keywords: Dirac quantum field
zbMATH Keywords: globally hyperbolic spacetime
zbMATH Keywords: nuclearity
zbMATH Keywords: local equivalence
zbMATH Keywords: split property
MaRDI profile type: Publication
OpenAlex ID: W2027692290
arXiv ID: math-ph/0106028
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DOI: 10.1007/S00220-005-1398-2
description: scientific article