= Scalar electrodynamics three-point vertex
{title2=$V_3^\mu=-ie(p+p')^\mu$}
= Scalar QED three-point vertex
{synonym}
Expanding the covariant scalar kinetic term gives $ieA_\mu(\phi\partial^\mu\phi^*-\phi^*\partial^\mu\phi)$. With $D=\partial+ieA$, the vertex for an incoming charged particle of momentum $p$ and an outgoing one of momentum $p'$ is $-ie(p+p')^\mu$. The antiparticle has the opposite charge-flow sign. The quadratic term $e^2A^2\phi^*\phi$ gives the separate <seagull vertex> $2ie^2\eta^{\mu\nu}$. On equal-mass external shells, contracting the three-point momentum with the photon momentum gives zero, the tree <scalar quantum electrodynamics Ward identity>.
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