Asymptotic morphisms and superselection theory in the scaling limit

TL;DR

This paper introduces a new approach using asymptotic morphisms to analyze superselection sectors in the scaling limit of quantum field theories, establishing a bijection with localized morphisms and exploring algebraic isomorphisms.

Contribution

It develops a variant of asymptotic morphisms for scaling limit theories and links them to superselection sectors, extending the algebraic framework of quantum field theory.

Findings

Unitary equivalence classes of scaling limit morphisms correspond to asymptotic morphism pairs.

Quasi-local C*-algebras of different nets are isomorphic under broad conditions.

Constructs an extension of the scaling algebra with a rich representation on the limit Hilbert space.

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.