In a nonperturbative formulation, radiative corrections arising from Lorentz and CPT violation in the fermion sector induce a definite and nonzero Chern-Simons addition to the electromagnetic action. If instead a perturbative formulation is used, an infinite class of theories characterized by the value of the Chern-Simons coefficient emerges at the quantum level.
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Jackiw et al. (1999) studied this question.
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