JournalsjncgVol. 8, No. 3pp. 735–770

Asymptotic morphisms and superselection theory in the scaling limit

  • Roberto Conti

    Università di Roma “La Sapienza”, Roma, Italy
  • Gerardo Morsella

    Università di Roma “Tor Vergata”, Italy
Asymptotic morphisms and superselection theory in the scaling limit  cover
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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.

Cite this article

Roberto Conti, Gerardo Morsella, Asymptotic morphisms and superselection theory in the scaling limit . J. Noncommut. Geom. 8 (2014), no. 3, pp. 735–770

DOI 10.4171/JNCG/169