Exploring Free and Interaction Terms of L in Quantum Field Theory

[steve1763]

TL;DR Summary

What are the Feynman diagrams associated with the generating function of this free scalar field Lagrangian?

With free part L=-½(∂Φ)^2 -½m^2 Φ^2
and interaction term L=½gΦ^2


Any help would be appreciated, thank you.

 

[vanhees71]

You have only a vertex with two legs. It's obvious that you get the exact solution by resumming Dyson's equation for the two-point Green's function, i.e., $G=G_0+G_0 \Sigma G$ with the self-energy $\Sigma$ which is trivial in this case. You know of course what you must get, namely a free particle with mass $M$ with $M^2=m^2-g$.