Charged Quantum Fields Associated with Endomorphisms of CAR and CCR Algebras
Quasi-free endomorphisms of the CAR and CCR algebras are studied from the point of view of the theory of superselection sectors.
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arXiv subjects
Carsten Binnenhei
Publications and source records attributed to Carsten Binnenhei.
Implementation of Endomorphisms of the CAR Algebra
The implementation of non-surjective Bogoliubov transformations in Fock states over CAR algebras is investigated. Such a transformation is implementable by a Hilbert space of isometries if and only if the well-known Shale-Stinespring condition is met. In this case, the dimension of the implementing Hilbert space equals the square root of the Watatani index of the associated inclusion of CAR algebras, and both are determined by the Fredholm index of the corresponding one-particle operator. Explicit expressions for the implementing operators are obtained, and the connected components of the semigroup of implementable transformations are described.
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On The Even CAR Algebra
We exhibit a family of *-isomorphisms mapping the CAR algebra onto its even subalgebra.
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$O_\infty$ Realized on Bose Fock Space
We study the semigroup of Bogoliubov endomorphisms of the canonical commutation relations which give rise to representations of the Cuntz algebra $O_\infty$ on Fock space and describe the corresponding Cuntz algebra generators in detail.
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