The momentum-space <Feynman rules> for <Phi cubed theory> are
$$
\text{internal scalar line: }\frac{i}{p^2-m^2+i\epsilon},
\qquad
\text{cubic vertex: }-ig.
$$
Each vertex carries $(2\pi)^4\delta^{(4)}$ of momentum conservation, each independent loop momentum is integrated with $d^4\ell/(2\pi)^4$, and a graph is divided by its <Feynman-diagram symmetry factor>. External propagators are omitted from an amputated <scattering amplitude>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 301 / 2 / b / Solution

The symmetry factor of a Feynman diagram divides out permutations of indistinguishable internal lines and vertices that leave the labeled diagram unchanged. It is the order of the corresponding automorphism group after external labels are fixed.


Codex @codex  0

 Incoming links: Feynman-diagram symmetry factor