Given a local Haag-Kastler net of von Neumann algebras and one of its scaling limit states, we introduce a variant of the notion of asymptotic morphism by Connes and Higson, and we show that the unitary equivalence classes of (localized) morphisms of the scaling limit theory of the original net are in bijection with classes of suitable pairs of such asymptotic morphisms. In the process, we also show that the quasi-local C*-algebras of two nets are isomorphic under very general hypotheses, and we construct an extension of the scaling algebra whose representation on the scaling limit Hilbert space contains the local von Neumann algebras. We also study the relation between our asymptotic morphisms and superselection sectors preserved in the scaling limit.

Conti, R., Morsella, G. (2014). Asymptotic morphisms and superselection theory in the scaling limit. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 8(3), 735-770 [10.4171/JNCG/169].

Asymptotic morphisms and superselection theory in the scaling limit

MORSELLA, GERARDO
2014-01-01

Abstract

Given a local Haag-Kastler net of von Neumann algebras and one of its scaling limit states, we introduce a variant of the notion of asymptotic morphism by Connes and Higson, and we show that the unitary equivalence classes of (localized) morphisms of the scaling limit theory of the original net are in bijection with classes of suitable pairs of such asymptotic morphisms. In the process, we also show that the quasi-local C*-algebras of two nets are isomorphic under very general hypotheses, and we construct an extension of the scaling algebra whose representation on the scaling limit Hilbert space contains the local von Neumann algebras. We also study the relation between our asymptotic morphisms and superselection sectors preserved in the scaling limit.
2014
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Conti, R., Morsella, G. (2014). Asymptotic morphisms and superselection theory in the scaling limit. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 8(3), 735-770 [10.4171/JNCG/169].
Conti, R; Morsella, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/121856
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