# Do photons have angular momentum along their direction of motion?

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?

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