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I am reading Ramond and in page 112 he says "In $\lambda \phi^{4}$ theory, diagrams can be at most three-particle reducible". My question:

  1. whether the individual Feynman Diagrams are treated as particles or not?

  2. Are the dinosaur and sunset diagrams 2 and 3 particle reducible respectively?

  3. What does $n$-particle reducible mean?

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A n-particle reducible diagram is a diagram that can be cut into two pieces if one cuts n or less lines. Conversely, a n-particle irreducible (n-PI) diagram cannot be cut into two pieces if one cuts n lines.

The sunset diagram is 3-particle reducible, since it has 3 internal lines, but it is both 1-PI and 2-PI, and contributes to the self-energy (which contains 1-PI diagrams) and when closed, to the Luttinger-Ward functional (that contains all vacuum 2-PI diagrams).

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  • $\begingroup$ So the terminology has no relation whatsoever with treating Feynmann diagrams as particles ? $\endgroup$
    – Abhishek Pal
    Commented Nov 2, 2015 at 11:39
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    $\begingroup$ @AbhishekPal: Feynamn diagrams never represent particles. The particles here a the virtual particles represented by the lines in the diagram. $\endgroup$
    – Adam
    Commented Nov 2, 2015 at 11:40
  • $\begingroup$ Hi Adam. Do you mean that in general only 1-PI diagrams contribute to self-energy? $\endgroup$
    – Veronica Noordzee
    Commented Sep 4 at 20:21
  • $\begingroup$ @VeronicaNoordzee yes $\endgroup$
    – Adam
    Commented Sep 5 at 6:46
  • $\begingroup$ Okay, thank you! $\endgroup$
    – Veronica Noordzee
    Commented Sep 6 at 13:26

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