arXiv subjects

Jens Böckenhauer

Publications and source records attributed to Jens Böckenhauer.

3 recordsLinked to original sources

arXiv1996

Superselection Sectors of $\son$ Wess-Zumino-Witten Models

The superselection structure of $\son$ WZW models is investigated from the point of view of algebraic quantum field theory. At level $1$ it turns out that the observable algebras of the WZW theory can be constructed in terms of even CAR algebras. This fact allows to give a formulation of these models close to the DHR framework. Localized endomorphisms are constructed explicitly in terms of Bogoliubov transformations, and the WZW fusion rules are proven using the DHR sector product. At level $2$ it is shown that most of the sectors are realized in $\HNSh=\HNS\otimes\HNS$ where $\HNS$ is the Neveu-Schwarz sector of the level $1$ theory. The level $2$ characters are derived and $\HNSh$ is decomposed completely into tensor products of the sectors of the WZW chiral algebra and irreducible representation spaces of the coset Virasoro algebra. Crucial for this analysis is the DHR decomposition of $\HNSh$ into sectors of a gauge invariant fermion algebra since the WZW chiral algebra as well as the coset Virasoro algebra are invariant under the gauge group $\Oz$.

hep-th↗

arXiv1995

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 $\varrho_1^{\rm loc}$ 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.

hep-th↗

arXiv1994

Decomposition of Representations of CAR Induced by Bogoliubov Endomorphisms

In a Fock representation, a non-surjective Bogoliubov transformation of CAR leads to a reducible representation. For the case that the corresponding Bogoliubov operator has finite corank, the decomposition into irreducible subrepresentations is clarified. In particular, it turns out that the number of appearing subrepresentations is completely determined by the corank.

hep-th↗