On the effective action of the vacuum photon splitting in Lorentz violating QED through Krein space

The finding of an explicit effective action describing amplitude of photon triple splitting is investigated through Krein space quantization and quantum metric fluctuation. Using the derivative expansion method, the one-loop radiative corrections from Lorentz- and CPT- violating extended Krein QED shows that it is not possible to find a nonzero effective action.