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We consider Abelian vector-field models in the presence of the Wess-Zumino interaction with pseudoscalar matter. The occurrence of the dynamic breaking of Lorentz symmetry at classical and one-loop levels is described for massless and massive vector fields. This phenomenon appears to be the nonperturbative counterpart of the perturbative renormalizability and/or unitarity breaking in chiral gauge theories.
Andrianov et al. (Mon,) studied this question.