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

{title2=$\phi^3$ theory}

Phi cubed theory has interaction $-g\phi^3/3!$, giving a cubic vertex $-ig$. In four spacetime dimensions the scalar field has mass dimension one and $g$ has mass dimension one.


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 Incoming links: Phi cubed theory