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

Asymptotic morphisms and superselection theory in the scaling limit