  The renormalization of quantum field theories usually assumes Lorentz and
gauge symmetries, besides the general restrictions imposed by unitarity and
causality. However, the set of renormalizable theories can be enlarged by
relaxing some of these assumptions. In this work, we consider the particular
case of a CPT-preserving but Lorentz-breaking extension of scalar QED. For this
theory, we calculate the one-loop radiative corrections to the three- and
four-point scalar-vector vertex functions, at the lowest order in the Lorentz
violation parameters; and we explicitly verify that the resulting low-energy
effective action is compatible with the usual gauge invariance requirements.
With these results, we complete the one-loop renormalization of the model at
the leading order in the Lorentz-violating parameters.
