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

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In summary, the conversation discusses the concept of 1 particle irreducible (1PI) diagrams in QFT and their contribution to a 4 point-function. The individual is confused about why only one specific 1PI graph is mentioned in the text and asks if other diagrams, such as those shown in QFT2.png and QFT3.png, also contribute. The response explains that while these diagrams do contribute, they are of higher order in perturbation theory and the author is likely focusing on a specific loop order.
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Malamala
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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!
 

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  • #2
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.
 

1) What is 1PI in a 4-point function?

The 1PI (one-particle-irreducible) part of a 4-point function is the connected part of the diagram that cannot be separated into two smaller diagrams. It represents the contribution of virtual particles to the scattering process.

2) How is 1PI calculated in a 4-point function?

1PI can be calculated using Feynman diagrams, which represent the different possible interactions between particles. The 1PI part is obtained by removing all external lines from the diagram and summing over all possible internal lines.

3) What is the significance of 1PI in a 4-point function?

The 1PI part of a 4-point function is important as it contains the dominant contribution to the scattering process. It also helps to simplify calculations by reducing the number of diagrams that need to be considered.

4) How does 1PI in a 4-point function relate to renormalization?

In quantum field theory, renormalization is the process of removing divergences from calculations. 1PI diagrams are used in renormalization schemes as they allow for a more efficient treatment of divergences.

5) Can 1PI in a 4-point function be measured experimentally?

While 1PI itself cannot be directly measured, it can be inferred from experimental data by comparing theoretical predictions with observed results. This allows for the testing and validation of theoretical models.

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