Superselection in the presence of constraints

TL;DR

This paper investigates how superselection sectors in quantum systems are affected by constraints, extending existing theory to include systems with nontrivial centres and applying it to a QED-inspired model.

Contribution

It generalizes Doplicher-Roberts superselection theory to systems with constraints and nontrivial centres, analyzing the conditions for superselection structures to persist.

Findings

Superselection structures can survive certain constraints under specific conditions.

The theory is exemplified through a model inspired by interacting QED.

Conditions for compatibility between constraints and superselection are established.

Abstract

For systems which contain both superselection structure and constraints, we study compatibility between constraining and superselection. Specifically, we start with a generalisation of Doplicher-Roberts superselection theory to the case of nontrivial centre, and a set of Dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form. This involves an analysis of the restriction and factorisation of superselection structures. We develop an example for this theory, modelled on interacting QED.