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Localized endomorphisms of the chiral Ising model

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Abstract

Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms ϱ loc1 and ϱ loc1/2 . It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence π0 ο ϱ loc1 ≊ π1 and π0 ο ϱ loc1/2 ≊ π1/2 holds. Araki's formalism of the selfdual CAR algebra is used for the proof. We prove local normality and extend representations and localized endomorphisms to a global algebra of observables which is generated by local von Neumann algebras on the punctured circle. In this framework, we manifestly prove fusion rules and derive statistics operators.

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  1. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761, Hamburg

    Jens Böckenhauer

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  1. Jens Böckenhauer
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Communicated by H. Araki

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Böckenhauer, J. Localized endomorphisms of the chiral Ising model. Commun.Math. Phys. 177, 265–304 (1996). https://doi.org/10.1007/BF02101894

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