Hello, PF have helped me a lot understanding a lot of important things in physics, I hope you guys can help me with this too :). I have problems understand the symmetry groups. I know there are groups like SU(2), O(3).. etc. But I have no idea how they represent certain particles. So particles are characterized by spin (0, 1, 1/2...) at which the spin of a particle gets represented by the SO(3) subgroup which 'forms' the corresponding field. But A) Where does 'SO(3)' comes from? B) Each group represents a certain spin; for example: for spin 1/2. We need to rotate over 720° to get the 'same' particle (can't find the exact English term right now :X). But how do I know which rotation corresponds to which spin? C) How does this all connect to symmetry breaking?