Scalar electrodynamics

In theoretical physics, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field that takes the place of the Dirac fermions in "ordinary" quantum electrodynamics. The scalar field is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the Abelian Higgs mechanism.

The model consists of a complex scalar field ${\displaystyle \phi (x)}$ minimally coupled to a gauge field ${\displaystyle A_{\mu }(x)}$. The dynamics is given by the Lagrangian density

${\displaystyle {\mathcal {L}}=(D_{\mu }\phi )^{*}D^{\mu }\phi -U(\phi ^{*}\phi )-{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\ ,}$

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