Feynmann diagrams interpretation and diagramm symmetry order

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Discussion Overview

The discussion revolves around the interpretation of Feynman diagrams, particularly in relation to virtual particles and the concept of symmetry factors. Participants explore how these diagrams represent physical processes and the implications of dividing by symmetry order in calculations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on how the interpretation of Feynman diagrams as representations of virtual particles aligns with the necessity to divide by symmetry order.
  • Another participant explains that symmetry factors arise from overcounting in calculations, referencing Wick's theorem to illustrate that a single diagram can correspond to multiple terms in the expansion, thus necessitating division.
  • Some participants express confusion about reconciling the mathematical treatment of diagrams with their physical interpretation, suggesting that Feynman diagrams should not be viewed as literal representations of physical processes.
  • There is a consensus among some participants that Feynman diagrams are terms in an expansion and that their interpretation can be misleading if taken too literally.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical treatment of symmetry factors and the implications of Wick's theorem, but there remains uncertainty regarding the compatibility of these mathematical concepts with the physical interpretation of Feynman diagrams.

Contextual Notes

Some participants note limitations in understanding how the mathematical framework aligns with physical interpretations, highlighting that the discussion does not resolve these complexities.

kvl
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I'm trying to understand Feynman diagrams interpretation in terms of virtual particles. What I still can't understand is how this interpretation is compatible with the fact that one should divide each diagram by its symmetry order.

As far as I understand, diagram symmetry order means how many different physical processes are represented by this diagram. But than one should multiply the probability by this number, not divide !

Probably someone can clarify this a bit...
 
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Yeah, symmetry factors are a b&tch! What you have to remember is that they come from an OVERCOUNTING, so you have to divide. You can see this by explicitly looking at Wick's theorem - a single feynman diagram can represent MANY terms in the Wick expansion, and we only want one of these terms. That's why we divide.

I've been doing loop calculations for years, and just last week, my collaborator corrected me on my symmetry factors! I doubt I'll ever get them right first-time! :cry:
 
blechman said:
Yeah, symmetry factors are a b&tch! What you have to remember is that they come from an OVERCOUNTING, so you have to divide. You can see this by explicitly looking at Wick's theorem - a single feynman diagram can represent MANY terms in the Wick expansion, and we only want one of these terms. That's why we divide.
Yes, I understand the Wick's theorem and why we should divide. But what I don't understand is how can it be compatible with interpretation of diagrams in terms of virtual particles creation/anihilation !
 
kvl said:
how can it be compatible with interpretation of diagrams in terms of virtual particles creation/anihilation !

Feynman diagrams are literally terms in an expansion.

It is misleading to think these are diagrams of actually what is happening.
 
masudr said:
Feynman diagrams are literally terms in an expansion.

It is misleading to think these are diagrams of actually what is happening.

I agree. The point is that a feynman diagram overcounts the number of ways lines can attach to vertices. And this is the symmetry factor.
 
masudr said:
Feynman diagrams are literally terms in an expansion.

It is misleading to think these are diagrams of actually what is happening.

Wick theorem used for "external connection" (as shown in Peskin &Schroeder books) shows that your interpretation is correct.
 

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