# Contents

## Idea

Given a local net of observables

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

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

Localized endomorphisms play a central role in DHR superselection theory.

## Definition

###### Definition

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

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