Localized endomorphisms of the chiral Ising model

Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms rho(1)(loc) and rho(1/2)(loc). It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence pi(0) circle rho(1)(loc) congruent to pi(1) and pi(0) circle rho(1/2)(loc) 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.