How to compute the number of loops in a Feynman diagram?

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Discussion Overview

The discussion revolves around the computation of the number of loops in Feynman diagrams, particularly in the context of \(\phi^{3}\) theory and its application in quantum field theory (QFT). Participants explore the implications of vertices, internal and external lines, and the complexities introduced by multiple interaction vertices, such as those found in the Standard Model.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether there is a general algorithm for counting loops in Feynman diagrams, especially when multiple interaction vertices are involved.
  • Another participant discusses the nature of the \(\lambda \phi^{3}\) theory, emphasizing that self-interaction does not imply particle creation or annihilation but rather pure scattering of identical particles.
  • There is a mention of A. Zee's arguments against certain theories involving different powers in \(\phi\), suggesting a critical perspective on the theoretical framework.
  • Participants express confusion regarding the appropriate subforum for discussing QFT-related questions, with some arguing that such topics should be included under Quantum Physics rather than General Physics.
  • One participant highlights that questions about renormalization and loop counting are central to the QFT experience, indicating the complexity and technicality involved in Feynman diagram computations.

Areas of Agreement / Disagreement

Participants express differing views on the categorization of the thread and the appropriateness of discussing QFT topics in the chosen subforum. There is no consensus on a general algorithm for counting loops, and the discussion remains unresolved regarding the classification of the \(\lambda \phi^{3}\) theory.

Contextual Notes

Participants reference specific theoretical frameworks and concepts without reaching a definitive conclusion on the methodology for counting loops in Feynman diagrams. The discussion includes assumptions about the nature of self-interaction and the classification of physical theories.

lonelyphysicist
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In doing my [tex]\phi^{3}[/tex] theory I didn't know exactly how to count the number of loops in a diagram given the number of vertices, internal and external lines. Is there a general algorithm in doing this? What if we have more than one interaction vertex (e.g. the Standard Model)?

PS. What does it mean when it says my thread has been "moved"?
 
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lonelyphysicist said:
PS. What does it mean when it says my thread has been "moved"?

It means an administrator thought that it better belonged to another subforum. If you talk about the "physical mass" thread, I'd like to know why it was moved, because I don't think it is really a college-level question !

cheers,
Patrick.
 
It's nonphysical [itex]\lambda \phi^{3}[/itex].The vertex (the OPI Green function of 4 points in the first order of perturbation theory) is made up of 3 scalar bosons.Self interaction doesn't mean creating/annihilating particles (that means there's no emission,nor absorption of particles),but only pure scattering (identical particles scattering one off another).

Read Zee's [1] argument against this theory and others involving other powers in [itex]\phi[/itex].

Daniel.

---------------------------------------------------
[1] A.Zee,"Quantum Field Theory in a Nutshell",PUP,2003.
 
dextercioby said:
It's nonphysical [itex]\lambda \phi^{3}[/itex].The vertex (the OPI Green function of 4 points in the first order of perturbation theory) is made up of 3 scalar bosons.Self interaction doesn't mean creating/annihilating particles (that means there's no emission,nor absorption of particles),but only pure scattering (identical particles scattering one off another).

Read Zee's [1] argument against this theory and others involving other powers in [itex]\phi[/itex].

Do you mean my thread was moved because [itex]\lambda \phi^{3}[/itex] is not a physical theory? :smile:
 
No,no,you had put in the wrong forum.It's Quantum Physics related and it should have been posted here.:smile: General Physics is not for such specific problems.

Daniel.
 
Dexter is this a general rule that QFT math questions go in quantum mechanics? Why not particles?
 
Under the "Quantum Physics" forum link it says "Quantum Mechanics and Field Theory" - that's why I posted my questions here.

Anyone who knows some QFT would know that these questions do form the bulk of the QFT experience. Renormalization, for instance, is all about the technicalities - how many loops, how to get rid of the large logs, what subtraction scheme to use, etc. Feynman diagram computation itself involves lots of machinery too.
 

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