A Question about Spin Induced Magnetic Moment

[qinglong.1397]

Does photon has spin induced magnetic moment? I think the answer is no. But why? You know, electron has. Does this have something to do with the fact that electron is massive while photon massless?

 

[Bill_K]

Primarily, it's because the electron is a charged particle and the photon is not.

 

[qinglong.1397]

Some guy says it has something to do with photon's charge conjugation quantum number. If you have two photons' wave function $$\Psi_{p,\sigma}, \Psi_{p',\sigma'}$$, you can couple them to a electromagnetic current to measure the interaction and magnetic moment:

$$(\Psi_{p',\sigma'},J^\mu\Psi_{p,\sigma})$$

But RHS has charge conjugation number +1 while LHS has charge conjugation number -1. So it's zero!

I couldn't understand charge conjugation quantum number, though this theory sounds fancy.