Physical meaning of whole state space for spin-one

Question

The spin-one quantum states belong to $\mathbb{C}^3$, with a set of orthonormal bases taken as the spin component along a direction, which would correspond to the direction of the magnetic fild gradient in a Stern-Gerlach apparatus. So we have a sample space (observable) with clear physics for each direction; but any $SU(3)$ transformation turns a sample space into another, leaving plenty of room for other observables - check the Gell-Mann matrices.

The question is: if a massive elementary particle ($W^\pm$, $Z^0$) is described intrinsically (by itself) with $\mathbb{C}^3$, what do the rest of sample spaces, the "observables" not identified with a spin projection, stand for? I consider the case of nonzero mass just to put aside the issues of the speed of light limit, but massless gauge fields should be understood as well.

Answer 1

I think this problem is connected to the fact that all known massive elementary particles are spin-half - with $SU(2)$ representing rotations, all sample spaces are spin projections - or zero, except the electroweak massive bosons, being these formulated as massless gauge fields.

An intrinsic quantum state space - with all sample spaces representing intrinsic properties - cannot be assigned to an elementary massive particle with spin greater than $\tfrac{1}{2}$, such kind of particles do not make sense by themselves; one has to consider at least a decay or "vertex" event, add more elements to the scenario.