# Feynman rules for a general Lagrangian

How do I find the Feynman rules for a general Lagrangian density?

For example the Lagrangian $$L = \partial_\mu \psi \partial^\mu \psi +a \psi\partial_\mu \psi \partial^\mu \psi+b \psi^2 \partial_\mu \psi \partial^\mu \psi.$$

Lagrange-Euler equation is: $$\Box \psi(1+2a \psi+2b\psi^2)=-a\partial_\mu \psi \partial^\mu \psi -2b \psi \partial_\mu \psi \partial^\mu \psi.$$ Obviously there's no interaction term like $$\phi^3$$ or $$\phi^4$$, so there's no the X vertex appearing in the rules, but how about the other rules how do these change?

And how to find them?

• You write down the propagator and calculate every single term :p – gented May 28 at 12:38