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The photon, being a vector boson has 2 spin states, $\pm 1$.

In relativity, we can determine the four-spin vector $s^{\mu}$ of a particle (see e.g. Costa et al. 2017).

What would $s^{\mu}$ be for a photon? How does it relate to the 2 spin states?

Thanks

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There is no such thing as a rest frame for a photon, so there is no such thing as a 4-spin in the sense of the Wikipedia article you link.

In fact, there is no such thing as spin for a photon, cf. also this answer of mine for a lengthy elaboration on how the properties of masslessness, being a gauge boson and having no true "spin" are all basically equivalent. Massless particles are characterized by helicity, not spin, the "2 spin states" should more precisely be called "2 helicity states".

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