# Detailed calculation of the scattering amplitude between two particles in $\phi^4$-perturbation theory using the path integral formalism

I'm looking for detailed example/calculation of the scattering amplitude between two particles (mesons) in $\phi^4$-perturbation theory using the path integral formalism. Do anyone of you guys have a good example to share? Maybe some old exercise of yours or a link to the web.

I'm using the book Quantum Field theory in a Nutshell and I'm currently reading chapter 1.7 (Feynman Diagrams) and I really wish there was a more detailed description of the calculations for the scattering amplitude of collision between particles. That's why I think an example would be of great educational help to me.

## 2 Answers

Have you checked the book by David Bailin and Alexander Love on Gauge Theories? https://www.amazon.com/Introduction-Revised-Graduate-Student-Physics/dp/075030281X It contains the essence on scattering amplitudes all starting from the Green functions formalism which uses path integrals (thus no operators, no Wick theorem).

Does the calculation starting from page 129 of this note by Casalbuoni is of any help to you? As far as I have understood question, it may help you out.

Also, Critical properties of $\phi^4$ theories by Hagen Kleinert is the most extensive reference for $\phi^4$ theory that I know of. Not widely known, at least in my experience, is a treasure trove for higher-order loop calculations, finding symmetry factor etc. Highly recommended for non-trivial details which are not easy to find elsewhere.