Gottfried and Yan's Quantum Mechanics has the following discussion of photon angular momentum:

$$ \boldsymbol{J}_\textbf{sp}= -i\hbar\sum_ka^\dagger_k\times a_k = \hbar \sum_{k\lambda} \lambda \hat{\boldsymbol{k}} \, n_{k\lambda}.$$

"Hence the one-photon state of of momentum $\hbar\boldsymbol{k}$ has angular momentum $\pm\hbar$ along $\boldsymbol{k}$, that is to say the photon has helicity $\pm1$. Note the striking difference from nonrelativistic angular momentum: the spin has no component along the direction of motion."

This seems to me to be directly contradicting itself. Does the photon have angular momentum along its direction of motion?

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  • $\begingroup$ As an aside, the spacing on my last term seems bad. Is there a better way to do that? $\endgroup$ – NoethersOneRing Dec 25 '16 at 23:29
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    $\begingroup$ You can use \, in LaTeX to insert a small space, as I have demonstrated in an edit. $\endgroup$ – JamalS Dec 26 '16 at 0:26

Yes, it does. I think they meant to say "the spin has no component perpendicular to the direction of motion."

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