Abstract
Given its superselection sectors with non-abelian braid group statistics, we extend the algebraA of local observables into an algebra ℱ containing localized intertwiner fields which carry the superselection charges. The construction of the inner degrees of freedom, as well as the study of their transformation properties (quantum symmetry), are entirely in terms of the superselection structure of the observables. As a novel and characteristic feature for braid group statistics, Clebsch-Gordan and commutation “coefficients” generically take values in the algebra ℳ of symmetry operators, much as it is the case with quasi-Hopf symmetry.A, ℱ, and ℳ are allC * algebras, i.e. represented by bounded operators on a Hilbert space with positive metric.
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Communicated by H. Araki
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Rehren, KH. Field operators for anyons and plektons. Commun.Math. Phys. 145, 123–148 (1992). https://doi.org/10.1007/BF02099283
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DOI: https://doi.org/10.1007/BF02099283