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On the relation between types of local algebras in different global representations

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Abstract

LetA,A(O), ℝd, α be a theory of local observables. We show that there are relations between the Connes-von Neumann types of the algebras belonging to a different global representation. For example if one representation is the vacuum representation such that the wedge algebra is of type III1 then this also is the case for other representations, provided these are connected with the vacuum by large translations.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Göttingen, Bunsenstrasse 9, W-3400, Göttingen, Federal Republic of Germany

    H. -J. Borchers

  2. Karl-Weierstrass-Institut für Mathematik der Akademie der Wissenschaften, Mohrenstrasse 39, 1086, Berlin, Federal Republic of Germany

    M. Wollenberg

Authors
  1. H. -J. Borchers
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  2. M. Wollenberg
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Communicated by K. Gawedzki

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Borchers, H.J., Wollenberg, M. On the relation between types of local algebras in different global representations. Commun.Math. Phys. 137, 161–173 (1991). https://doi.org/10.1007/BF02099121

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  • DOI: https://doi.org/10.1007/BF02099121

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