Scalar quantum electrodynamics (Scalar QED)

Scalar quantum electrodynamics minimally couples a complex scalar field to the electromagnetic gauge field through $D_{\mu }={\partial }_{\mu }+ie{A}_{\mu }$.

The scalar-QED term $e^2{A}_{\mu }{A}^{\mu }{\varphi }^{\ast }\varphi$ produces a local two-photon two-scalar vertex, conventionally called the seagull vertex.