$A^\mu$ can have multipole expansions in classical electrodynamics. This gives rise to dipole photon, quadrupole photon etc. For dipole photon $j=1$ (In electrodynamics books they write it as $l=1$). Since, $\vec J=\vec L+\vec S$ and $j=|l-s|$ to $|l+s|$, in steps of unity.
Can we apply this formula because I think S is not a good quantum number to specify photons but helicity is. If it propagates in z-direction then $S_z$ is good quantum number. Right? Then, can I directly use this formula or should I instead use $m_j=m_l+m_s$? Does it mean whenever I have gamma-transitions between two nuclear levels I should always use $m_j=m_l+m_s$ and not use $\vec J=\vec L+\vec S$ and $j=|l-s|$ to $|l+s|$?
We know that, the projection $S_z=0$ is not allowed for a photon propagating along z-direction. But is it true that $L_z=0$ projection is also not allowed for photons?