Renormalized Feynmann Rules (derivation)

[JCCJ]

I'm studing the basics of renormalization (with phi^4 theory) and once you write the renormalized lagrangian with the counterterms, how do you derive the feynmann rules asociated to the kinetic counterterm?

---∅--- = i(p^2 δ Z - δ m) How??...

 

[The_Duck]

Do you know how to derive the Feynman rule for e.g. the phi^4 interaction turn? You can treat the two counterterms $\delta_m \phi^2$ and $\delta_Z \partial_\mu \phi \partial^\mu \phi$ as new interactions, and derive the associated Feynman rules for the vertices they produce in the same way you derive the Feynman rule for the familiar phi^4 interaction term.

 

[JCCJ]

Thanks!
Yes I did it,
I was puzzled because at first glance it seemed to me arbitrary regard this kinetic counterterm as part of the interaction hamiltonian and the standar kinectic term not, but I have clarified myself.