Generation of Carroll-Field-Jackiw term in the Functional Integral approach within Horava-Lifshitz $z=3$ CPT-violating QED

In this paper, we apply the functional integral methodology to induce the Carroll-Field-Jackiw (CFJ) term in Horava-Lifshitz $z=3$ CPT-violating QED, where Lorentz and CPT breaking for fermion and photon sectors is introduced, and show that the CFJ term is finite but undetermined.