Solve Lagrangian Deduc Vertex Problem Easily

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I want deduc vertex of the lagrangian, but I not know how?
 
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If you mean, which particles interact you just have look at the interacting terms of the Lagrangian. In general just look at the ones that aren't kinetic or mass terms.

To calculate the associated Feynman rule just keep the term add an "i" and remove the fields. If you have a vertex with 3 or 4 vector bosons the Feynman rule is bit more complicated because you have to take into account the different ways in which they can interact. Check it out for example in Peskin pag 507.
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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