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Angular momentum operators for bosons

  1. Jan 11, 2012 #1
    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.
  2. jcsd
  3. Jan 11, 2012 #2


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    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. :smile: Massless bosons work the same way: they're still vectors.
  4. Jan 12, 2012 #3


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