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 βα ∂σF σβ ∂ λ F λα , i.e., it possesses two additional derivatives coupled to a CPT -even tensor D βα 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.

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In this paper, we consider an electrodynamics of higher derivatives coupled to a Lorentz-violating background tensor. Specifically, we are interested in a dimension-five term of the CPT -odd sector of the nonminimal Standard-Model Extension. By a particular choice of the operatorkAF , we obtain a higher-derivative version of the Carroll-Field-Jackiw (CFJ) term, 1 2 κλµν A λ Dκ Fµν , with a Lorentz-violating background vector Dκ. This modification is subject to being investigated. We calculate the propagator of the theory and from its poles, we analyze the dispersion relations of the isotropic and anisotropic sectors. We verify that classical causality is valid for all parameter choices, but that unitarity of the theory is generally not assured. The latter is found to break down for certain configurations of the background field and momentum. In an analog way, we also study a dimension-five anisotropic higher-derivative CFJ term, which is written as κλµν A λ Tκ(T ·∂) 2 Fµν and is directly linked to the photon sector of Myers-Pospelov theory. Within the second model, purely timelike and spacelike Tκ are considered. For the timelike choice, one mode is causal, whereas the other is noncausal. Unitarity is conserved, in general, as long as the energy stays real -even for the noncausal mode. For the spacelike scenario, causality is violated when the propagation direction lies within certain regimes. However, there are particular configurations preserving unitarity and strong numerical indications exist that unitarity is guaranteed for all purely spacelike configurations. The results improve our understanding of nonminimal CPT-odd extensions of the electromagnetic sector.Here, we also stated the general structure of individual terms. A generic dimensionless background tensor with a set X of Lorentz indices is indicated by n X whereÔ X is a field operator with the same set of Lorentz indices. The mass dimension of the background has been extracted explicitly to show the dependence on the scales M QG and M . The remaining Lagrange density δL other contains all additional contributions that have not been taken into account previously. These could be nonperturbative in nature. According to the perturbative series of Eq. (1), the nonminimal SME is a natural extension of the higher-derivative Lorentz-invariant contributions in the same sense as the minimal SME is an extension of the SM. Searching for physics beyond the SM via an effective theory, there is a priori no reason why such nonminimal terms should be discarded. Interpreting these terms as theories that are valid within a certain energy range only, power-counting nonrenormalizability is not considered to be a problem.Due to the arguments explained above, individual terms have an energy dependence of the form (E/M QG ) d−4 and (E/M ) d−4 , respectively. Nonminimal contributions grow with energy, i.e., after a certain point they dominate the minimal ones. Therefore, they might be essential in experiments involving particles of high energies, e.g., cosmic rays. From the ...