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Index of subfactors and statistics of quantum fields. I

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Abstract

We identify the statistical dimension of a superselection sector in a local quantum field theory with the square root of the index of a localized endomorphism of the quasi-local C*-algebra that represents the sector. As a consequence in a two-dimensional theory the possible values of the statistical dimension below 2 are restricted to a given discrete set.

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Authors and Affiliations

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

    Roberto Longo

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  1. Roberto Longo
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Communicated by A. Connes

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

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Longo, R. Index of subfactors and statistics of quantum fields. I. Commun.Math. Phys. 126, 217–247 (1989). https://doi.org/10.1007/BF02125124

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  • DOI: https://doi.org/10.1007/BF02125124

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