We consider scalar quantum electrodynamics in the Higgs phase and in the presence of Lorentz violation. Spontaneous breaking of the gauge symmetry gives rise to Lorentz-violating gauge field mass terms. These may cause the longitudinal mode of the gauge field to propagate superluminally. The theory may be quantized by the Faddeev-Popov procedure, although the Lagrangian for the ghost fields also needs to be Lorentz violating.

• Received 1 March 2012

DOI:https://doi.org/10.1103/PhysRevD.86.045008