Graduate Understanding 1PI Diagrams and the Role in 4-Point Functions in QFT Explained

[Malamala]

Hello! I am reading Schwarz's QFT and he introduces 1 particle irreducible (1PI) diagram, which is basically defined as a diagram which can't be divided into non-trivial smaller diagram by removing (cutting) a single line. I thought I understood it, but then he introduces the 4 point-function and he says (in chapter 21.1) that the only 1PI graph contributing to a 4 fermionic function in the one attached in QFT1.png. I am not sure I understand why that is the only one. Can't we have something like the stuff in QFT2.png and QFT3.png (sorry for my bad drawing)? They are indeed higher order in the perturbation, but they still contribute to the 4 point function. Thank you!

 

[Orodruin]

Sure you can, but the diagrams you are asking about are all of higher order in perturbation theory. Scwartz is likely working at loop order.

I don’t have Schwartz here, but when you put the fermion arrows on the fermion lines there should be two diagrams. The one you show here and the one where the photobs make a cross. I will try to remember to have a look when I get to my office.