localized endomorphism

**algebraic quantum field theory** (perturbative, on curved spacetimes, homotopical)

**field theory**: classical, pre-quantum, quantum, perturbative quantum

Given a local net of observables

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

a natural algebra endomorphism

$\rho : \mathcal{A} \to \mathcal{A}$

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.

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)