Localized endomorphisms of the chiral Ising model
Year: 1996
Type: preprint
Abstract: Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms ̺ loc 1 and ̺ loc 1/2. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence π0 ◦ ̺ loc 1 ∼ = π1 and π0 ◦ ̺ loc 1/2 ∼ = π1/2 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. 1
Author: Böckenhauer, Jens
Institution: Universität Hamburg
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3099559537