Dimensional reduction of a Lorentz- and<i>CPT</i>-violating Maxwell-Chern-Simons model

Abstract

Taking as a starting point a Lorentz and CPT noninvariant Chern-Simons-like model defined in $1+3$ dimensions, we proceed to realize its dimensional reduction to $D=1+2.$ One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector ${v}^{\ensuremath{\mu}}.$ In spite of breaking Lorentz invariance in the particle frame, this model may preserve CPT symmetry for a single particular choice of ${v}^{\ensuremath{\mu}}.$ Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitarity of the gauge sector is assured without any restriction, while the scalar sector is unitary only in the spacelike case.