# Physical meaning of whole state space for spin-one

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.

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.