This past year I took a QFT class and I now feel comfortable solving scattering problems, but I am still a bit perplexed by how physicists write down a Lagrangian in the first place. In particular, given some particle menu, is there a method for writing down the most general Lagrangian interaction terms?
It would be very helpful if someone could provide a concrete example, say if you had 1 fermion field and 1 vector boson field, what are all of the possible interaction terms (including non-renormalizable terms)?
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