Feynman diagrams with odd number of vertices.

In summary, the conversation discusses the interference that occurs in Feynman diagrams with odd numbers of vertices, specifically in the case of electron-electron scattering and the emission of a photon. It is mentioned that there is no significant difference in this interference at all orders, and one photon emission is not necessarily suppressed due to interference. However, there is a theorem that allows for the omission of a diagram with an odd number of photon vertices. The topic is further explored with the example of electron-electron scattering and the possibility of one photon emission being suppressed.
  • #1
Spinnor
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If we scatter unpolarized electrons off each other and we calculate the amplitude for electrons to scatter into final states and one photon to be emitted do we get destructive interference because the photon can be emitted by either electron? Is one photon emission suppressed in favor of an even number of photons?

Can we say anything interesting about amplitudes representing Feynman diagrams with odd number of vertices?

Thanks for any help!
 
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  • #2
I honestly don't think there is anything "special" about Feynman diagram with odd number of vertices in QED, but I could be wrong.
In the case of a process like [itex]e^+e^-\to e^+e^-\gamma[/itex] you always have interference between different diagrams. The idea is that the photon could be emitted both by the positron or by the electron and both before or after the scattering. Since these diagrams produce all the same final state, by quantum mechanics they are indistinguishable processes and therefore they interfere.

However, a similar thing happen to all orders, not necessarily in the case of just one photon or odd numbers of vertices.

From my naive point of view there no big difference, unless some non-trivial reason comes out.
 
  • #3
Spinnor said:
Can we say anything interesting about amplitudes representing Feynman diagrams with odd number of vertices?
Only when a diagram has odd number of photon vertices attached to a electron loop,in that case you can omit the diagram altogether.It is Furry's theorem.
 
  • #4
Einj said:
I honestly don't think there is anything "special" about Feynman diagram with odd number of vertices in QED, but I could be wrong.
In the case of a process like [itex]e^+e^-\to e^+e^-\gamma[/itex] you always have interference between different diagrams. The idea is that the photon could be emitted both by the positron or by the electron and both before or after the scattering. Since these diagrams produce all the same final state, by quantum mechanics they are indistinguishable processes and therefore they interfere.

However, a similar thing happen to all orders, not necessarily in the case of just one photon or odd numbers of vertices.

From my naive point of view there no big difference, unless some non-trivial reason comes out.

Does argument change much if the reaction were e- + e- ---> e- + e- + γ?

I'm curious if one photon emitted when electrons scatter is suppressed because if interference?

Thanks for your help!
 
  • #5
I think the same reasoning can be applied also to electron-electron scattering. Why do you think that it should be suppressed? Do you have any hint on that?
 

FAQ: Feynman diagrams with odd number of vertices.

1. What are Feynman diagrams with odd number of vertices?

Feynman diagrams are graphical representations of mathematical expressions used to calculate the probability of interactions between elementary particles. The number of vertices in a Feynman diagram corresponds to the number of particles involved in the interaction. An odd number of vertices indicates that the interaction involves an odd number of particles.

2. How are Feynman diagrams with odd number of vertices used in particle physics?

Feynman diagrams with odd number of vertices are used to calculate the probability of interactions involving one or three particles, such as scattering or decay processes. They provide a visual representation of the mathematical calculations involved in these interactions.

3. Can Feynman diagrams with odd number of vertices be used for interactions involving more than three particles?

No, Feynman diagrams with odd number of vertices are limited to interactions involving one or three particles. For interactions involving more particles, diagrams with even number of vertices are used.

4. What is the significance of odd number of vertices in Feynman diagrams?

The odd number of vertices in Feynman diagrams represents the conservation of charge, energy, and momentum in the interaction. Each vertex represents an interaction between particles, and the overall number of vertices must be odd for these conservation laws to hold.

5. Are Feynman diagrams with odd number of vertices applicable in all types of interactions?

Yes, Feynman diagrams with odd number of vertices can be used in all types of interactions, including electromagnetic, weak, and strong interactions. They provide a universal framework for understanding and calculating particle interactions.

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