Superselection in the presence of constraints

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.