Unitarity in higher-order Lorentz-invariance violating QED

The unitarity in Lorentz invariance violating QED consisting of standard fermions and higher-order photons of the Myers-Pospelov theory is studied. We find ghost states associated to the higher-order character of the theory which could render the $S$ matrix nonunitary. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to preserve unitarity.