Quantum constraints

This is a review of the main features of the program of quantum constraints developed by Hurst, Grundling et al. Specifically, we develop the mathematical structures implied by a state selection condition of the type ω(C*C)=0 in a C*-algebra framework. We consider internal compatibility questions for a constraint set, compatibility conditions of constraints with group actions (and the 3-cocycles arising from implementation issues), and compatibility with space-time locality. For examples, we consider linear bosonic constraints, and Gupta-Bleuler electromagnetism.