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

In summary: So, on the whole, it would not be surprising if QFT math questions generally ended up in the QM forum.
  • #1
lonelyphysicist
32
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
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:
 
  • #5
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.
 
  • #6
Dexter is this a general rule that QFT math questions go in quantum mechanics? Why not particles?
 
  • #7
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.
 

1. How do I determine the number of loops in a Feynman diagram?

The number of loops in a Feynman diagram can be determined by counting the number of closed lines in the diagram. These closed lines represent virtual particles and each one counts as a loop. For example, a diagram with two closed lines would have two loops.

2. Can the number of loops in a Feynman diagram change?

Yes, the number of loops in a Feynman diagram can change depending on the specific process being represented. Some processes may have more interactions between particles, resulting in more loops, while others may have fewer interactions and therefore fewer loops.

3. How does the number of loops affect the calculation of particle interactions?

The number of loops in a Feynman diagram is directly related to the complexity and strength of particle interactions. More loops represent more interactions between particles, which can result in stronger or more complicated interactions. This is taken into account when calculating the probability of a specific particle interaction occurring.

4. Why are loops important in Feynman diagrams?

Loops in Feynman diagrams represent virtual particles, which are important for understanding the behavior of subatomic particles. These virtual particles are not observed directly, but their effects can be observed through the interactions they have with other particles. The number of loops in a Feynman diagram affects the strength and complexity of these interactions.

5. Are there any shortcuts for counting loops in a Feynman diagram?

Yes, there are some shortcuts that can be used to determine the number of loops in a Feynman diagram. For example, the number of loops can be equal to the number of vertices in the diagram minus the number of external particles. Additionally, for diagrams with multiple closed lines, the number of loops can be determined by dividing the total number of closed lines by 2. However, it is still important to understand the underlying concepts and be able to count loops manually for more complex diagrams.

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