I'm studying Quantum Field Theory and the main books I'm reading (Peskin and Schwartz) present Feynman diagrams something like this: one first derive how to express with perturbation theory the [itex]n[/itex]-point correlation functions, and then represent each term by a diagram. It is then derived the Feynman rules that allows one to do the backwards process: given a diagram, find out the terms in the expansion.(adsbygoogle = window.adsbygoogle || []).push({});

The point that all books make, at least in my opinion, is: computing the expansion is hard and using Wick's theorem is quite hard, so one develops these Feynman rules so that the process becomes: (1st) find the Feynman diagrams and (2nd) associate the number to the diagrams according to the rules.

My whole question is: considering a particular interaction lagrangian, how does one finds the Feynman diagrams up to some specific order?

It obviously isn't by expanding the [itex]n[/itex]-point function, because if it was there would be no point in drawing the diagrams anyway, since the expansion would already be known.

The only thing I can figure out is that in the expansion of the [itex]n[/itex]-point each diagram has [itex]n[/itex] external points and expansion to order [itex]\lambda^k[/itex] will have [itex]k[/itex] internal points.

So considering for example the [itex]\mathcal{L}_{\mathrm{int}} = \lambda \phi^4/4![/itex] theory, how can I find the Feynman diagrams up to order [itex]\lambda^2[/itex]?

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# A How does one find the Feynman diagrams?

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