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One-particle irreducible diagrams are diagrams that cannot be broken into two disconnected diagrams by cutting an internal propagator.


  1. Why are the external lines on an one-particle irreducible diagram truncated/amputated?

  2. What is the motivation for the word 'one-particle' in the terminology?

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  • $\begingroup$ 1. The amputation of lines has nothing to do with the diagrams being 1PI, so I'm not sure what you mean. 2. Questions about the origin/motivation of terminology should go to History of Science and Mathematics, cf. this meta post, since you have no guarantee at all that there is a physical reason for any particular turn of phrase. $\endgroup$
    – ACuriousMind
    Feb 15 '17 at 20:07
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  1. It is a convention that simplifies some formulas. You can always choose to include the propagators on the external lines, but their effect is rather trivial so they don't add relevant information to the diagram.

  2. "One particle" means "one line". The reason for the word "particle" is that lines represent particles (sometimes, virtual particles). The reason for the word "one" is that the diagrams remains connected after cutting any one line. You can also have two-particle irreducible, if it remains connected after cutting any two lines, and more generally, $n$-particle irreducible if it remains connected after cutting any $n$-lines.


Remark: in $1.)$ I am assuming that you are using Feynman diagrams to calculate correlation functions. If you are using them to calculate $S$-matrix elements, then the external lines are amputated because of the LSZ theorem.

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