No radiative corrections to the Carroll–Field–Jackiw term beyond one-loop order

Abstract

We demonstrate explicitly the absence of the quantum corrections to the Carroll–Field–Jackiw (CFJ) term beyond one-loop within the Lorentz-breaking CPT-odd extension of QED. The proof holds within two prescriptions of quantum calculations, with the axial vector in the fermion sector treated either as a perturbation or as a contribution in the exact propagator of the fermion field.