nLab
localized endomorphism

Contents

Idea

Given a local net of observables

𝒜:Open(X)Algebras \mathcal{A} : Open(X) \to Algebras

a natural algebra endomorphism

ρ:𝒜𝒜 \rho : \mathcal{A} \to \mathcal{A}

is called local or localized if outside of a bounded region of spacetime XX it is the identity?.

Localized endomorphisms play a central role in DHR superselection theory.

Definition

Definition

An endomorphim ρ\rho is localized or localizable if there is a bounded open set 𝒪𝒥\mathcal{O} \in \mathcal{J} such that ρ\rho is the identity on the algebra of the causal complement 𝒜(𝒪 )\mathcal{A}(\mathcal{O}^{\perp}). Such an endomorphism is localized in 𝒪\mathcal{O}.

Created on December 1, 2011 12:37:21 by Urs Schreiber (134.76.83.9)