Coupling order in Fenman diagrams

In summary, the speaker is asking if it is possible to have two identical vertices with different coupling strengths. They then provide an example of a toy Lagrangian and explain how the two vertices would be combined into one with a sum of the coupling constants. They also mention the concept of taylor expansion and how the leading order vertex may not always be the leading order diagram.
  • #1
Neitrino
137
0
Sorry if this appears a basic question,
but could you pls advise me is it possible to have a two identical vertexes but with different strength coupling?

I have some toy Lagrangian and when I calculate Feynman rules I get for one vertex following expression:

(M1+M2)*(combination of fields )+M1(combination of fields).

Where M1 and M2 are coupling strength, so if I want to calculate some process in some order I should consider diagrams of the same order with respect to the coupling strenght. And in my case I am calculating diagrams with respect to M2 strength coupling... so does it mean that for my vertex I should extract only M2 coupling part from that general vertex which wrote above: (M1+M2)*(combination of fields ) - > (M2)*(combination of fields ) ?
 
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  • #2
Just forgotten to mention (combination of fields) exactly the same . . . so identical field combinations in two vertex but different coupling strength . . .
 
  • #3
If I understand correctly you have two identical terms in the lagrangian, just different coefficients( coupling constants). Just add the terms into one, and you have one vertex with a coupling constant that is the sum of the two.
 
  • #4
Think about it as a taylor expansion. What is small?

If you're expanding in the fact that M2 is small, like you would in QED , then remember the leading order vertex is just M1, and the subleading the combination.

But remember! Just because a VERTEX is subleading does not mean the DIAGRAM is subleading. (If you're expanding in coupling strength I believe its the same, but if you end up expanding in mass or momenta you can end up with powers canceling due to different vertices as well as propagators.)
 

What is coupling order in Feynman diagrams?

Coupling order refers to the strength of the interaction between particles in a Feynman diagram. It is determined by the coupling constant, which represents the strength of the force responsible for the interaction between particles.

How is coupling order represented in Feynman diagrams?

Coupling order is represented by the number of vertices in a Feynman diagram. Each vertex represents an interaction between particles, and the number of vertices corresponds to the coupling order. For example, a diagram with three vertices has a coupling order of three.

What is the significance of coupling order in Feynman diagrams?

Coupling order is important because it affects the probability of the interaction occurring between particles. A higher coupling order means a stronger interaction and a higher probability of the particles interacting with each other.

How does coupling order impact the accuracy of Feynman diagrams?

The accuracy of a Feynman diagram is affected by the coupling order because it determines the number of terms needed in the calculation of the scattering amplitude. A higher coupling order requires more terms, making the calculation more complex and potentially less accurate.

Can coupling order be changed in a Feynman diagram?

Yes, coupling order can be changed by altering the coupling constant. This can be done by changing the energy or momentum of the particles involved in the interaction, or by introducing new particles with different coupling constants.

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