Representations of nets of C*-algebras over S^1

TL;DR

This paper explores new types of representations for nets of C*-algebras over the circle, demonstrating their existence and covariance properties, especially in the context of curved spacetime and fundamental group effects.

Contribution

It introduces a novel notion of representations for nets of C*-algebras over S^1 and proves their existence and covariance under certain groups.

Findings

Any net of C*-algebras over S^1 admits faithful representations.

Covariant nets under Diff(S^1) admit representations covariant under any amenable subgroup.

The approach accounts for the effects of the fundamental group in curved spacetime contexts.

Abstract

In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account of the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C*-algebras over S^1 admits faithful representations, and when the net is covariant under Diff(S^1), it admits representations covariant under any amenable subgroup of Diff(S^1).