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In this paper, we investigate an electrodynamics in which the physical modesare coupled to a Lorentz-violating (LV) background by means of ahigher-derivative term. We analyze the modes associated with the dispersionrelations (DRs) obtained from the poles of the propagator. More specifically,we study Maxwell's electrodynamics modified by a LV operator of mass dimension6. 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 fixedbackground. We first evaluate the propagator and obtain the dispersionrelations of the theory. By doing so, we analyze some configurations of thefixed background and search for sectors where the energy is well-defined andcausality is assured. A brief analysis of unitarity is included for particularconfigurations. Afterwards, we perform the same kind of analysis for a moregeneral dimension-6 model. We conclude that the modes of both Lagrangedensities are possibly plagued by physical problems, including causality andunitarity violation, and that signal propagation may become physicallymeaningful only in the high-momentum regime.

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