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Nets of Subfactors | | R.Longo
; K.-H.Rehren
; | | Date: |
10 Nov 1994 | | Journal: | Rev.Math.Phys. 7 (1995) 567-598 | | Subject: | hep-th | | Abstract: | A subtheory of a quantum field theory specifies von~Neumann subalgebras $aa(oo)$ (the `observables’ in the space-time region $oo$) of the von~Neumann algebras $b(oo)$ (the `fields’ localized in $oo$). Every local algebra being a (type $III_1$) factor, the inclusion $aa(oo) subset b(oo)$ is a subfactor. The assignment of these local subfactors to the space-time regions is called a `net of subfactors’. The theory of subfactors is applied to such nets. In order to characterize the `relative position’ of the subtheory, and in particular to control the restriction and induction of superselection sectors, the canonical endomorphism is studied. The crucial observation is this: the canonical endomorphism of a local subfactor extends to an endomorphism of the field net, which in turn restricts to a localized endomorphism of the observable net. The method allows to characterize, and reconstruct, local extensions $b$ of a given theory $aa$ in terms of the observables. Various non-trivial examples are given. | | Source: | arXiv, hep-th/9411077 | | Services: | Forum | Review | PDF | Favorites | |
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