  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.
