From Renormalization talk/idea by Sean Carroll, when he talks about effective field theory:

but then I could construct from that the following diagram with four lines in it enter image description here

In previous talks he explained a bit about diagrams and told interactions can be represented by many (even infinite) number of diagrams. Additionally he mentions "in" lines can be changed to "out" ones (anti-particle), but for one particular interaction, the number of external lines remains the same. Above he claims to construct a 4 external legs interaction from a 3 one. What does it mean?

ADDED more context from the video:

let's imagine you only had Phi cubed in your field theory that would lead to a Feynman diagram that is just this little vertex but then I could construct from that the following diagram with four lines in it... so for the effective field theorist you don't have a choice when you start writing down terms in your Lagrangian you have to include them all as long as they don't violate some symmetry or something

  • $\begingroup$ What is an "in+out line"? $\endgroup$ Jan 5, 2021 at 3:56
  • $\begingroup$ @NiharKarve I think he means “in or out” as in 4 external lines. Looks like Carroll is showing something about the effective potential. $\endgroup$
    – kaylimekay
    Jan 5, 2021 at 4:06
  • 1
    $\begingroup$ Imagine cutting each side of that box, you'd then have four copies of your three legged diagram. $\endgroup$
    – Triatticus
    Jan 5, 2021 at 4:46
  • $\begingroup$ @Triatticus, indeed looks like it. Why do you think it is what Sean refers to? $\endgroup$ Jan 5, 2021 at 5:12
  • $\begingroup$ @kaylimekay, thank you. I've edited the question to make it more "correct". $\endgroup$ Jan 5, 2021 at 5:17


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