# Homework Help: How to deduce the Feynman rules?

1. Dec 26, 2017

### Mr rabbit

1. The declaration of the problem, all variables and data given / known

Calculate the decay amplitude of $\pi ^ 0$ in an electron-positron pair $\pi^0 \rightarrow e^+ e^-$, assuming that the interaction is of the form

$\mathcal {L}_{int} = g \: \partial_{\mu} \phi \: \overline{\psi} \: \gamma ^ {\mu} \: \gamma^5 \: \psi$

where g is a coupling constant, $\phi$ is the scalar field corresponding to $\pi^0$ and $\psi$ is the electron field.

2. Relevant equations

3. The attempt of a solution

I don't know how to deduce in general the Feynman rules for a given Lagrangian. We made some examples with some theories ($\phi^4$, scalar Yukawa, QED scalar, QED) but for example the term $\partial_{\mu} \phi$ confuses me

2. Dec 31, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Jan 4, 2018

### vanhees71

How does the interaction term look in energy-momentum space, i.e., for fields $\propto \exp(-\mathrm{i} x \cdot p)$?

4. Jan 4, 2018

### MathematicalPhysicist

I think this appears in Drell and Bjorken the Fields textbook.