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Nuclearity, Local Quasiequivalence and Split Property for Dirac Quantum Fields in Curved Spacetime

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Abstract

We show that a free Dirac quantum field on a globally hyperbolic spacetime has the following structural properties: (a) any two quasifree Hadamard states on the algebra of free Dirac fields are locally quasiequivalent; (b) the split-property holds in the representation of any quasifree Hadamard state; (c) if the underlying spacetime is static, then the nuclearity condition is satisfied, that is, the free energy associated with a finitely extended subsystem (``box'') has a linear dependence on the volume of the box and goes like ∝T s +1 for large temperatures T, where s+1 is the number of dimensions of the spacetime.

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Author notes

  1. Stefan Hollands

    Present address: Georg-August Universität at Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany

Authors and Affiliations

  1. Dipartimento di Mathematica, Università di Roma ``Tor Vergata'', Via della Ricerca Scientifica, 00133, Roma, Italy

    Claudio D'Antoni

  2. Department of Physics, Enrico Fermi Institute, University of Chicago, 5640 Ellis Ave., Chicago, IL, 60367, USA

    Stefan Hollands

Authors
  1. Claudio D'Antoni
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  2. Stefan Hollands
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Communicated by H. Araki

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D'Antoni, C., Hollands, S. Nuclearity, Local Quasiequivalence and Split Property for Dirac Quantum Fields in Curved Spacetime. Commun. Math. Phys. 261, 133–159 (2006). https://doi.org/10.1007/s00220-005-1398-2

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  • DOI: https://doi.org/10.1007/s00220-005-1398-2

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