 Scalar quantum electrodynamics Ward identity

The scalar Ward identity relates the charged-scalar photon vertex to differences of inverse scalar propagators. At tree level, contraction with photon momentum $q=p^{\prime }-p$ usesIncluding the appropriate charge and vertex conventions makes the right side the difference of inverse free propagators. The full identity uses the dressed vertex and full inverse propagators instead.

Scalar quantum electrodynamics also contains a two-photon contact interaction from the square of the gauge covariant derivative. Its coefficient is tied to the one-photon and kinetic terms by gauge invariance. Consequently, checks of scalar scattering must include both sequential one-photon attachments and the contact term. Renormalization conventions preserving the symmetry retain these relations between the coefficients.