Maxwell electrodynamics modified by CPT-even and Lorentz-violating dimension-6 higher-derivative terms

Abstract: In this paper, we investigate an electrodynamics in which the physical modes are coupled to a Lorentz-violating (LV) background by means of a higher-derivative term. We analyze the modes associated with the dispersion relations (DRs) obtained from the poles of the propagator. More specifically, we study Maxwell's electrodynamics modified by a LV operator of mass dimension 6. The modification has the form ${D_{\beta\alpha}}\partial_{\sigma}F^{\sigma\beta}\partial_{\lambda} F^{\lambda\alpha}$, i.e., it possesses two additional derivatives coupled to a \textit{CPT}-even tensor $D_{\beta\alpha}$ that plays the role of the fixed background. We first evaluate the propagator and obtain the dispersion relations of the theory. By doing so, we analyze some configurations of the fixed background and search for sectors where the energy is well-defined and causality is assured. A brief analysis of unitarity is included for particular configurations. Afterwards, we perform the same kind of analysis for a more general dimension-6 model. We conclude that the modes of both Lagrange densities are possibly plagued by physical problems, including causality and unitarity violation, and that signal propagation may become physically meaningful only in the high-momentum regime.