Communications in Mathematical Physics

, Volume 145, Issue 1, pp 123–148 | Cite as

Field operators for anyons and plektons

  • Karl-Henning Rehren
Article

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.

Keywords

Neural Network Statistical Physic Hilbert Space Complex System Characteristic Feature 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Karl-Henning Rehren
    • 1
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburg 50Federal Republic of Germany

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