Four-leg vertex of a factorial-normalized scalar interaction
= Four-leg vertex of a factorial-normalized scalar interaction
{title2=$V_4=i\lambda$}
An interaction $\mathcal L_{\rm int}=+\lambda\phi^4/4!$ produces a four-leg momentum-space vertex $i\lambda$. The $4!$ assignments of external legs cancel the coefficient factorial. With a negative interaction sign the vertex is $-i\lambda$. Graph <Feynman-diagram symmetry factors> are a separate combinatorial issue.