How Do Spin and Polarization Relate to Photon States?

[Pacopag]

Homework Statement

I'm trying to derive the stefan-Boltzmann law by considering a box of photons (as in Landau and Lifgarbagez and other texts). At one point in the derivation we multiply the density of states by 2 in order to account for the two independent polarizations of a photon. But at what point do we account for the fact that the spin of the photon is 1, so we have the "three" independent spin states, -1, 0, and 1? Or is there a relationship between "spin" and "polarization" that no one told me about?

Homework Equations

The number of states with frequency between w and w+dw is
$$2 V d^3w \over (2\pi)^3$$
V is the volume of the box, the rest of the stuff is from the phase space volume element and
the factor 2 out front accounts for the two polarizations.

The Attempt at a Solution

I read an older post about helicity of a photon. The poster mentioned something about a photon not being found in a spin 0 state. I didn't fully understand what he/she was saying. But it made me think that maybe 'polarity' and 'spin' are the same thing for a photon, and that the two polarities just correspond to two of the allowed spins while the third possible spin is just forbidden for some reason.

 

[krishna mohan]

As far as I understand, what you say is correct..there are three helicity states corresponding to the three spin states of the photon...makes sense since helicity is the projection of the spin along the momentum...and spin projections 1,0 and -1 corresponds to value of projection along, say, the z axis...If you take momentum along the z axis, both helicity and spin should correspond to the same thing...polarizations, on the other hand, are some linear combinations of the helicities...

I think there is some constraint due to masslessness which makes it only two independent helicities (only the transverse ones) for the photon ... a massive spin 1 particle should have 3 degrees of freedom...

Maybe you can look at chapter 6 of the book Quarks and Leptons by Halzen and Martin...