I What Insights Can the Feynman Diagram of γ+γ→γ+γ Provide?

ghbeefcake
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Photon photon scattering diagram
If you have γ+γ→γ+γ what would the Feynman diagram look like (time-ordering implied).

I think it will be a square with four photons on each vertex but is this all there is to it or am I missing something?
 
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ghbeefcake said:
am I missing something?
You're missing quite a lot. :oldsmile:
 
In leading order (fourth order perturbation theory) you have indeed box diagrams. There are 6 diagrams of this kind with all topologies of the external lines and two orientations of the loop. The remarkable property of the four-photon vertex is that it is superficially divergent but in fact convergent due to the Ward-Takahashi identities of em. gauge invariance. It's important to add all the 6 diagrams together to see the cancellation of the divergence.
 
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