Erratum: Dimensional reduction of a Lorentz- andCPT-violating Maxwell-Chern-Simons model [Phys. Rev. D67, 125011 (2003)]

Abstract

Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing 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 µ . In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of v µ . 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 space-like case.

Dual equivalence between self-dual and Maxwell-Chern-Simons models with Lorentz symmetry breaking

“…(2.7), which is fundamental to maintain the contents of the scalar sectors unchanged, thus, the gauge embedding generates the mass both for the vector field and for the matter field. Second, it includes the desired "mixed" scalar-vector term [11] φǫ µνρ v µ F νρ which earlier was obtained via dimensional reduction [12].…”

“…We can find a propagator in a manner similar to [13]. Indeed, the Lagrangian can be presented in the matrix form…”

“…Thus, we face a problem to obtain this operator, that is, to solve an equation P ∆ = 1. To do it, we use an ansatz similar to [13] 6) where…”

“…Imposing an appropriate gauge for the Maxwell-Chern-Simons theory and solving constraints for the self-dual theory, we can eliminate the irrelevant degrees of freedom corresponding to the nonphysical sector, thus remaining with the only physical particles whose dispersion relations in both theories look like E 2 = p 2 and E 2 = p 2 + m 2 , for two physical degrees of freedom. The detailed study of the unitarity and causality aspects of the Lorentz-breaking Maxwell-Chern-Simons theory (2.7) within which the nonphysical sector is shown to decouple, was carried out in [12] for the case of the M 2 = 0 which corresponds to the case of the light-like v µ , and can be straightforwardly generalized for the case M 2 = 0 (see also [19] for general issues related to the problems of unitarity and causality in Lorentz-breaking theories).…”

“…[6]) plays the role of the standard Lorentz-breaking theory whose different aspects were studied in [7] (nevertheless, the Lorentz breaking was studied also for other four-dimensional theories, such as, for example, linearized and non-linearized gravity [8]). At the same time, there is much less results for the Lorentz-breaking theories in other space-time dimensions, the only results are the study of compactification of the five-dimensional Lorentz-breaking theories [9], the study of two-dimensional Lorentz-breaking model for the scalar fields [10] and investigation of some phenomenological implications of the three-dimensional "mixed" scalar-vector quadratic term [11] which was earlier obtained via the dimensional reduction of the Jackiw term [12,13]. So, the natural problem is the investigation of more aspects of the lower-dimensional, especially three-dimensional, Lorentz-breaking field theories.…”