Exploring the Feynman Diagram of γ+γ→γ+γ: What Does It Reveal?

[ghbeefcake]

TL;DR Summary

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?

 

[strangerep]

am I missing something?

You're missing quite a lot.

 

[vanhees71]

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.