Böckenhauer, Jens

Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence 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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