Vacuum Cherenkov radiation and photon decay rates from generic Lorentz Invariance Violation

Among the most studied approaches to introduce the breaking of Lorentz symmetry, the generic approach is one of the most frequently used for phenomenology, it converges on the modification of the free particle dispersion relation. Using this approach in the photon sector, we have calculated the squared probability amplitude for vacuum Cherenkov radiation and photon decay by correcting the QED coupling at tree level and first order in LIV parameters. For the lower order energy correction we calculate the emission and decay rate for each process.