Angular momentum operators for bosons

[cygnet1]

I understand how the Pauli matrices can operate on the quantum state of an electron to obtain measurements of its intrinsic spin along the x, y and z axes. I also understand that since these matrices do not commute, it is impossible to determine what all three components were before measurment.

My question is this: What are the corresponding operators that measure the spin components of bosons? For massive bosons (like the W and Z), I imagine these operators would be 3x3 matrices, since there would be three possible values of spin (-1, 0, +1). For massless bosons (like the photon and gluon?), the operators would be 2x2, since 0-spin is not possible. Do these operators have a name, and do they commute?

Thank you in advance for any replies to this question, and please correct any errors I might have made in posing my question.

 

[Bill_K]

cygnet1, The general answer is that the matrices are the set of Clebsch-Gordan coefficients that couple together two representations of the rotation group. More specifically, spin 1 particles are vector particles, and the ways to couple two vectors A₁ and A₂ are quite familiar: A₁·A₂ forms spin 0, A₁ x A₂ forms spin 1, and spin 2 is the symmetric traceless tensor that's left over. Massless bosons work the same way: they're still vectors.

 

[Avodyne]

For massive bosons (like the W and Z), I imagine these operators would be 3x3 matrices, since there would be three possible values of spin (-1, 0, +1).

Yes.

For massless bosons (like the photon and gluon?), the operators would be 2x2, since 0-spin is not possible.

No, they're still 3x3, but in any allowed state, the amplitude of the 0 component (in the direction of the momentum) must vanish.