Maxwell electrodynamics modified by a CPT -odd dimension-five higher-derivative term

Abstract

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 ...

New Effects in the Vicinity of a Perfectly Conducting Plate in a Non-minimal Lorentz Violation Scenario

“…It would be very interesting to investigate what kind of physical phenomena could be produced by the presence of a conducting plate in the CPT-odd and non-minimal scenario proposed in [69,70], and compare the results with the ones obtained in the present work. In the model considered in [69,70], there is also a single background vector, as well as in the model (1).…”

Effects of CPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter

“…( 23) of Ref. [62], where this higher-derivative electrodynamics was examined in vacuo. It is important to point out that the remarkable difference between Eq.…”

“…In this context, the Myers-Pospelov model [59,60] was a pioneering proposal focusing on a dimension-five contribution. Recently, classical aspects of a modified, higher-derivative electrodynamics in vacuo were discussed in [61,62], including the derivation of the gauge propagator, the dispersion relations as well as an analysis of causality, unitary, and stability of the modes. Profound analyses were accomplished for the Maxwell-Podolsky electrodynamics modified by CPT -even, dimension-six terms [61] and for a CPT -odd, dimension-five electrodynamics [62], too.…”

“…Recently, classical aspects of a modified, higher-derivative electrodynamics in vacuo were discussed in [61,62], including the derivation of the gauge propagator, the dispersion relations as well as an analysis of causality, unitary, and stability of the modes. Profound analyses were accomplished for the Maxwell-Podolsky electrodynamics modified by CPT -even, dimension-six terms [61] and for a CPT -odd, dimension-five electrodynamics [62], too. Some nonminimal higher-derivative models have also been used to study the interaction energy between electromagnetic sources [63], the thermodynamic properties of electrodynamic systems [64], Horǎva-Lifshitz electrodynamics [65], and in the context of radiative corrections [66].…”

On perturbative aspects of a nonminimal Lorentz-violating QED with CPT-odd dimension-5 terms

“…However, it is clear that the quantum impacts of nonminimal couplings naturally need further studies. While a list of all possible LV vertices with dimensions up to 6 is presented in [5,6], it was shown in [19] that, although tree-level effects generated by many of these dimensions-5 and 6 vertices have been intensively studied, see, e.g., [20][21][22][23], only a few of such vertices have been really treated within the perturbative context up to now. The present study is aimed to follow this line, explicitly, to study the perturbative corrections in a nonminimal LV extended QED involving all CPT-odd dimension-5 operators proposed in [6].…”