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Communications in Mathematical Physics

, Volume 134, Issue 1, pp 139–196 | Cite as

Conformal field algebras with quantum symmetry from the theory of superselection sectors

  • Gerhard Mack
  • Volker Schomerus
Article

Abstract

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.

Keywords

Hilbert Space Field Operator Irreducible Representation Ising Model Quantum Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Gerhard Mack
    • 1
  • Volker Schomerus
    • 2
  1. 1.Mathematics DepartmentHarvard UniversityCambridgeUSA
  2. 2.II. Institut für Theoretische PhysikUniversität HamburgHamburg 50Germany

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