Lorentz and CPT violations from Chern-Simons modifications of QED

The possibility of a small modification of spinor Quantum Electro-Dynamics is reconsidered, in which Lorentz and CPT non-covariant kinetic terms for photons and fermions are present. The corresponding free field theory is carefully discussed. The finite one-loop parity-odd induced effective action is unambiguously calculated using the physical cutoff method, which manifestly encodes the maximal residual symmetry group allowed by the presence of the Lorentz and CPT breaking axial-vector. This very same induced effective action, which is different from those ones so far quoted in the Literature, is also re-derived by means of the dimensional regularization, provided the maximal residual symmetry is maintained in the enlarged $D$-dimensional space-time. As a consequence, it turns out that the requirement of keeping the maximal residual symmetry at the quantum level just corresponds to the physical renormalization prescription which naturally fixes the one-loop parity-odd induced effective action