The neutron is thought to consist of three tightly bound quarks, each with spin 1/2. Simple addition of angular momentum would tell us that the resulting system (neutron) could have either spin 1/2 or 3/2. So why does the neutron have spin 1/2 and not 3/2 (or a combination of both for that matter)?
I have knowledge of QM, group theory and classical field theory, so if possible I would like an answer in terms of these. If QFT is a necessity in the explanation though, then that's fine - I'll come back to this post after I learn it.