# How do we know how many Feynman diagrams to draw for a particular order?

For the purposes of this question, I'll limit the question to quantum electrodynamics, although this question could just as well be asked of electroweak theory and QCD.

For a particular order of perturbation theory, how do I know when I have drawn all the Feynman diagrams? For example, I have heard that in electron-electron scattering, at second order, we have t-channel and u-channel diagrams. But how did we know to draw these two channels - I would have stopped at just the t-channel diagram. And besides, if this is second order, what ever happened to first order diagrams of moller scattering?

One factoid I know about how many diagrams to draw is: in QED, a diagram that is third order in $$\alpha$$ has three vertices. Each vertex has one in-going and one out-going fermion and one virtual photon. A diagram that is fourth order in $$\alpha$$ has four vertices and so forth. I suppose I could use simple combinatorics to know when I've exhausted all the vertex combinations, but I don't know how to tell when two graphs are redundant, and there's still the t-channel and u-channel mystery as explained above.

• t-channel and u-channel diagrams are at first-order, too May 3, 2020 at 2:34
• Can you (or anyone else) please elaborate on that? The way I see it, all feynman diagrams that involve two-particle scattering should have both a t- and a u-channel diagram at all orders. But maybe I'm just imagining this. May 3, 2020 at 2:54
• it's challenging problem, but there are techniques to solve it, i'm no expert but see e.g., inspirehep.net/literature/315611 it seems to be quite a computer-sciency topic May 3, 2020 at 2:58
• There might be more modern descriptions in the FeynArts program manual, feynarts.de/FA3Guide.pdf May 3, 2020 at 2:59
• May 3, 2020 at 14:41