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Nuclear maps and modular structures II: Applications to quantum field theory

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Abstract

A correspondence between spectral properties of modular operators appearing in quantum field theory and the Hamiltonian is established. It allows to prove the “distal” split property for a wide class of models. Conversely, any model having this property is shown to satisfy the Haag-Swieca compactness criterion. The results lead to a new type of nuclearity condition which can be applied to quantum field theories on arbitrary space-time manifolds.

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Authors and Affiliations

  1. II. Institut für Theoretische Physik, Universität Hamburg, D-2000, Hamburg 50, Federal Republic of Germany

    Detlev Buchholz

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le A. Moro 5, I-00185, Roma, Italy

    Claudio D'Antoni

  3. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via Fontanile de Carcaricola, I-00133, Roma, Italy

    Roberto Longo

Authors
  1. Detlev Buchholz
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  2. Claudio D'Antoni
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  3. Roberto Longo
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Additional information

Communicated by H. Araki

Supported by the A. von Humboldt Stiftung, Bonn

Supported in part by Ministero della Pubblica Instruzione and CNR-GNAFA

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Buchholz, D., D'Antoni, C. & Longo, R. Nuclear maps and modular structures II: Applications to quantum field theory. Commun.Math. Phys. 129, 115–138 (1990). https://doi.org/10.1007/BF02096782

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  • DOI: https://doi.org/10.1007/BF02096782

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