QED-vacuum response and Cherenkov radiated energy in non-linear and Lorentz-symmetry violating scenarios

We explore the physical effects of non-linear electrodynamic coupled to parameters that indicate a violation of Lorentz-symmetry breaking (LSV). To do this, we consider a general non-linear photonic Lagrangian that is coupled to the Carroll–Field–Jackiw’s model (CFJ). Our investigation reveals how the constitutive properties of the vacuum and wave propagation are affected by the interference of the parameters LSV with the specific non-linear electrodynamic model under consideration. We also analyze the refractive indices for this new medium characterized by the coupling between non-linearities and the operators that carry the LSV message. Our results show that the QED-vacuum responds with birefringence and a dispersive propagation of waves. After that, we study the electromagnetic radiation produced by a moving charged particle interacting with this new medium. Our analysis shows that the emitted radiation is similar (resembles) to that of the Cherenkov effect for certain intensities of background magnetic fields. Finally, we compute the static potential profile within the framework of the gauge-invariant, but path-dependent, variables formalism. We find a logarithmic correction to the usual static Coulomb potential stemming from the LSV parameter, and there are also corrections due to the non-linearity. However, the logarithm behavior disappears whenever the LSV parameter is switched off.