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The possibility of a Chern-Simons- (CS-) like term generation in an extended model of QED, in which a Lorentz and CPT non-covariant kinetic term for fermions is present, has been investigated at finite temperature and in the presence of a background color magnetic field. To this end, the photon polarization operator in an external constant axial-vector field has been considered. One-loop contributions to its antisymmetric component due to fermions in the linear order of the axial-vector field have been obtained. Moreover, the first nontrivial correction to the induced CS term due to the presence of a weak constant homogeneous color magnetic field has been derived.
Эберт et al. (Mon,) studied this question.