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In this paper, we apply the functional integral methodology to induce theCarroll-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.

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