Let's say I want to calculate all connected 1-loop 4-point Feynman diagrams for a given interaction (in my case, with both $\phi^3$ and $\phi^4$ terms). Is there a way to lay out all the possible diagrams (and be sure that my list is complete) to apply Feynman's rules, or do I need to calculate their generating function and do it the "long" way?
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$\begingroup$ There is software to compute contributions to a given process, for example see this question: physics.stackexchange.com/q/96510 . Probably this is what you want for complicated processes. For relatively simple tree level or 1-loop diagrams (even 2 loops once you build up your intuition), you should be able to logic your way through every relevant diagram, and there are many worked examples in books. $\endgroup$– AndrewCommented Feb 16, 2021 at 18:30
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$\begingroup$ I was talking about 1-loop diagrams, forgot to put that in there. It's still not very intuitive for me, but I'm working toward that. Thanks for your input, I'll definitely hold on to that software suggestion! $\endgroup$– SotirisCommented Feb 16, 2021 at 18:44
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3$\begingroup$ does this answer your question? physics.stackexchange.com/q/304869/84967 $\endgroup$– AccidentalFourierTransformCommented Feb 16, 2021 at 18:47
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$\begingroup$ @Sotiris A useful thing to try is to understand simple cases and work your way up. It's a good idea to start with 1 loop, 1PI diagrams (1-particle irreducible) for $\varphi^4$. A few hints... first because of the $Z_2$ symmetry under $\varphi\rightarrow-\varphi$, correlation functions will vanish unless there is an even number of external lines. So start with 2 external legs, I'll tell you there is one 1-loop 1PI diagram. Can you draw it? There is also only one with 4 external leg, and indeed with 6. Try figuring the diagram for 2, 4, and 6 legs with 1 loop. Can you see why there aren't more? $\endgroup$– AndrewCommented Feb 16, 2021 at 19:14
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$\begingroup$ You both helped a lot, thank you! I think I have a good grasp of the subject matter now. $\endgroup$– SotirisCommented Feb 18, 2021 at 19:16
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