Undergrad Photon & Electron: Photoelectric & Compton Effects

[HAYAO]

But that's the problem: this "rough" description is too rough, because it leaves out all the quantum mechanics. Even at a heuristic level, the interaction is not properly described as one photon and one electron "colliding", because, in perturbative QFT terms:

(a) The lowest level Feynman diagram for this process has two vertexes, not one (since each vertex connects only three lines, the incoming/outgoing electron lines and the photon line, so to get a full diagram with a photon line coming in and a photon line going out, you need two vertexes);

(b) Making correct predictions about the actual experimental data requires more than just the lowest level Feynman diagram.

And, of course, Feynman diagrams are not really direct descriptions of processes happening in spacetime anyway. (For one thing, they're usually analyzed in momentum space.)

No doubt about it. Not that I know QFT like physicists, but there is no good classical analog to this interaction.

However, I believe that jeremyfiennes thinks there is only one type of fundamental interaction, which we need to clarify that it's not.