Using Furry's theorem, we know that the time ordered expectation value of odd number of currents in QED is zero. I was wondering taking into account Furry's theorem, will there be light by light scattering for the following process: $\gamma\gamma\gamma \rightarrow\gamma\gamma$?
Can someone please explain the above scenario?
Furry's theorem say's that there are no effective vertex that can poder your photon number by an odd number. Because of this, if you have a dyagram that goes from an even number to an odd number of photons, somewhere you will have an effective vertex that does that dirty thing, and you know it gives you a zero factor, so your dyagram amplitude is zero.
What you propose is not scattering as one photon is annihilated. Scattering can not do that. Also such reactions are indeed not possible. For example the reaction $\gamma\rightarrow \gamma \gamma $ is disallowed.
Light by light scattering is known as Delbrück scattering. It involves an even number of currents.
