Aspects of causality and unitarity and comments on vortexlike configurations in an Abelian model with a Lorentz-breaking term

The gauge-invariant Chern-Simons-type Lorentz- and $\mathrm{CPT}$-breaking term is here reassessed and a spin-projector method is adopted to account for the breaking (vector) parameter. Issues such as causality, unitarity, spontaneous gauge-symmetry breaking, and vortex formation are investigated, and consistency conditions on the external vector are identified.