Helicity is different form Spin for massless particle(photon)?

  1. As we know photon's helicity are [itex]\pm[/itex]1. Helicity is the projection of the spin S onto the direction of momentum, p, which is considered as Sz.
    What about Sx and Sy? They are both ZERO?
     
  2. jcsd
  3. Is it reasonable to say that massless particles have no spin but just helicity?
     
  4. Bill_K

    Bill_K 4,157
    Science Advisor

    What we mean by the spin of a particle is the subgroup of the Lorentz group that commutes with its 4-momentum (the "little group"). For a particle with mass, go to its rest frame where the 4-momentum is Pμ = (0,0,0,1) and the spin operators are the rotations in 3-space, Sx, Sy and Sz. They form SO(3).

    For a massless particle there is no rest frame, so take the 4-momentum in the z-direction, kμ = (0,0,1,1), and its spin operators are the three operators that preserve kμ.

    The first one is a rotation in the (x,y) plane. This is the helicity. It acts on the components of the particle's 4-potential as Ax ± iAy → ±(Ax ± iAy).

    The other two are null rotations, x → x + εk and y → y + εk. These operations just add a multiple of k to the 4-potential. But this is just a gauge transformation. So helicity is the only observable part.
     
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