I am still learning about all the Groups related to the Dirac Equation for spin 1/2 particles. Apparently, the reason that the Hilbert Space for spin 1/2 particles is 2-dimensional is because when you try to map SU(2) to SO(3), the mapping is 2-to-1, i.e. SU(2) is a double cover for SO(3). What about spin 1 particles. The spin vector space for those particles is 3-dimensional. Does that mean that SU(3) maps to SO(3) 1-to-1? As usual, thanks in advance.