On the effective action of the vacuum photon splitting in   Lorentz-violating QED
  We consider one-loop radiative corrections from Lorentz- and CPT- violating extended QED to address the specific problem of finding explicitly an effective action describing amplitude of photon triple splitting. We show that it is not possible to find a nonzero photon triple splitting effective action, at least by using the derivative expansion method (at zero external momenta), up to leading order in the Lorentz- and CPT- violating parameter. 
F. A. Brito, E. Passos and P. V. Santos
hep-th