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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Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
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