# How to compute the vertices from interaction lagrangian?

• Nakul Soni
In summary, The conversation discusses how to calculate the effective meson vertices for evaluating Feynman diagrams for meson scattering. The method involves looking for the piece proportional to the fields involved and adding the E propagator from the 2 point function. The conversation also mentions using QFT textbooks such as Peskin, Ashok Das, Itzykson & Zuber for guidance.
Nakul Soni
Hello all,
If I am having the the effective lagrangian which is actually free + interaction lagrangian (obtained from the minimal substitution for pseudoscalar and vector mesons). then how to compute the vertices of the interaction ?
I have taken into consideration of all symmetry breaking terms. How to construct the effective meson vertices to evaluate various feynman diagram for any meson scattering.

thank you

This should be explained in any QFT textbook and is no different from deriving the Feynman rules for the Lagrangian before symmetry breaking. What textbook are you using?

Hello
I am using Peskin, Ashok Das, Itzykson & zuber.
I understood that things.
But I am studying the scattering of mesons. In which I know the interaction lagrangian. Now from that how to calculate the lagrangian for different vertices.
For example I am studying A+B -> C+D. say by exchange of E mesons. I know total lagrangian which is Lo+Lint. So how to compute the lagrangian for AEC, BED vertices ?

Look for the piece proportional to the fields A E C, this will give you the vertex piece. Do the same for B E D, then you just have to add the E propagator from the 2 point function for E (from the kinetic piece and mass term for E if they exist)

Nakul Soni
RGevo said:
Look for the piece proportional to the fields A E C, this will give you the vertex piece. Do the same for B E D, then you just have to add the E propagator from the 2 point function for E (from the kinetic piece and mass term for E if they exist)
Hello
Thank you very much for the response
I will try this and will come back to you soon.
Thank you

## 1. How do I determine the number of vertices in an interaction Lagrangian?

The number of vertices in an interaction Lagrangian can be determined by counting the number of fields involved in the interaction. Each field represents one vertex in the Lagrangian.

## 2. How do I compute the Feynman rules for vertices in an interaction Lagrangian?

The Feynman rules for vertices can be computed by using the interaction terms in the Lagrangian and applying the relevant mathematical equations, such as the propagator and vertex factors, to determine the amplitude of the interaction.

## 3. Can I determine the strength of an interaction from the vertices in a Lagrangian?

Yes, the strength of an interaction can be determined by the coupling constants present in the interaction terms in the Lagrangian. The larger the coupling constant, the stronger the interaction.

## 4. How do I represent spin and momentum in a vertex from an interaction Lagrangian?

Spin and momentum are represented in a vertex by using the appropriate mathematical symbols, such as the spinor and momentum vectors, in the Feynman rules for the interaction. These symbols are then used in the calculation of the amplitude of the interaction.

## 5. Can I use the Feynman rules to compute vertices in a non-relativistic field theory?

No, the Feynman rules are specifically designed for relativistic field theories. In non-relativistic field theories, the vertices are computed using the appropriate non-relativistic versions of the Feynman rules, which take into account the differences in the mathematical equations.

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