= Two-photon vertex of a scalar field-strength interaction
{title2=$\mathcal A=\lambda[(q_1\cdot q_2)(\epsilon_1\cdot\epsilon_2)-(q_1\cdot\epsilon_2)(q_2\cdot\epsilon_1)]$}
The interaction $\lambda\Phi F_{\mu\nu}F^{\mu\nu}/4$ gives the displayed on-shell <scattering amplitude>, up to an overall phase, for a <scalar field> decaying to two <photons>. Substituting either <photon> <four-momentum> for its <polarization vector> makes the expression vanish, verifying its <Ward identity>. In the parent <rest frame>, summing the two physical transverse <photon polarizations> gives $\sum|\mathcal A|^2=|\lambda|^2M^4/2$. Including the <identical-particle factor in a final-state phase-space integral> gives $\Gamma=|\lambda|^2M^3/(64\pi)$.
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