Consider the partition function ##Z(\lambda)## of the ##0##-dimensional scalar ##\phi^{4}## theory(adsbygoogle = window.adsbygoogle || []).push({});

##Z(\lambda)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}d\phi\ \exp\{-\frac{1}{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}\}.##

It can be shown that

##Z(\lambda)=\sum\limits_{n=0}^{\infty}c_{n}\lambda^{n},##

where ##c_{n}=\frac{(-1)^{n}(2n-1)!!}{(4!)^{n}n!}.##

Can we instead propose a set of Feynman rules to compute the ##c_n##'s, or can Feynman rules only be written down for the correlation functions of the theory?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Feynman rules for a 0-dimensional field theory

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**