How to compute the vertices from interaction lagrangian?

[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

 

[Orodruin]

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?

 

[Nakul Soni]

Hello
Thank you for your response.
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 ?

Thank you in advance.

 

[RGevo]

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]

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