Localized Endomorphisms of the Chiral Ising Model

Details Localized Endomorphisms of the Chiral Ising Model Localized Endomorphisms of the Chiral Ising Model

1994-07-14

arxiv.org/abs/hep-th/9407079v2

Commun.Math.Phys. 177 (1996) 265-304

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, latex2e

Scientific paper

10.1007/BF02101894

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 $\pi_0\circ\varrho_1^{\rm loc}\cong\pi_1$ and $\pi_0\circ\varrho_{1/2}^{\rm loc}\cong\pi_{1/2}$ 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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