Before putting on the mathematical gloves, perhaps some ordinary English discussion of the likes of isotopic spin (isobaric spin or just isospin). From Wikipedia: G. t'Hooft, in the SciAm article I linked earlier, states that isospin symmetry is continuous. This means for instance that proton/neutron isospin can describe a particle in a superposition of proton + neutron. So what about the electric charge of +1 in the case of such a superposition? Or is it the case that, even though the symmetry is continuous, physically it doesn't exist?