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.
Categories: hep-th