Wick contraction and derivatives

Question

Hey guys, one quick question about Wick contractions and derivatives: Suppose I want to write down all (non-vacuum) Wick contractions of two fields a, and one field A into a cubic QCD-like interaction term of the form ∂νAμ,a(p1)abμ(p2)acν(p3)fabc to get the corresponding Feynman rule (where each field carries also a color index). How do I cope with the derivative? Normally I'd do a Fourier transform, but how do I know to which field the momentum belongs to? In other words if I Fourier trafo the derivative will it become a p1, p2, or p3?

Rudolf

Answer 1

There is a bit of discussion on how to do Fourier transforms in https://cadabra.science/qa/605/fourier-transform, but there are better ways now. I'll need a bit more time to write this up properly, but you can look in the tests/programming.cdb file if you are in a hurry (it's the test04 function which contains the logic).