Exact Calculation of the Radiatively Induced Lorentz and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">CPT</mml:mi></mml:math>Violation in QED

Radiative corrections arising from the axial coupling of charged fermions to a constant vector ${b}_{\ensuremath{\mu}}$ 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 ${b}_{\ensuremath{\mu}}$ 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.