Scalar electrodynamics
= Scalar electrodynamics
{title2=$\mathcal L=-\tfrac14f^2+|D\phi|^2-V(|\phi|^2)$}
A <charged scalar field> coupled to an Abelian <gauge field> through $D_\mu=\partial_\mu-iea_\mu$. Under $\phi\mapsto e^{i\alpha}\phi$ and $a_\mu\mapsto a_\mu+e^{-1}\partial_\mu\alpha$, its <gauge covariant derivative> transforms with the same phase. The potential determines whether the perturbative spectrum has a massless <photon> or exhibits the <Higgs mechanism>.