Exact Calculation of the Radiatively Induced Lorentz andCPTViolation in QED

Radiative corrections arising from the axial coupling of charged fermions to a constant vector $b_{\mu }$ can induce a Lorentz- and $\mathrm{CPT}$-violating Chern-Simons term in the QED action. We calculate the exact one-loop correction to this term keeping the full $b_{\mu }$ dependence, and show that in the physically interesting cases it coincides with the lowest-order result. The effect of regularization and renormalization and the implications of the result are briefly discussed.