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arXiv · hep-th/9407079

Localized Endomorphisms of the Chiral Ising Model

Jens Böckenhauer
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Abstract

Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms $\varrho_1^{\rm loc}$ and $\varrho_{1/2}^{\rm loc}$. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence $π_0\circ\varrho_1^{\rm loc}\congπ_1$ and $π_0\circ\varrho_{1/2}^{\rm loc}\congπ_{1/2}$ 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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Jens Böckenhauer. 1995-07-11. Localized Endomorphisms of the Chiral Ising Model. https://doi.org/10.1007/bf02101894

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