  We show that the correctly evaluated effective Lagrangian should include
short-distance interaction terms which have been avoided under the protection
of usual regularization and must be properly identified and reinstated if
regularization is to be removed. They have special physical and mathematical
significance as well as restoring gauge invariance and suppressing divergence
in the effective Lagrangian. The rich structure of the short-distance
interaction terms can open up challenging opportunities where the conventional
regularization with rigid structure is unavailable and inappropriate. It
becomes clear that gauge invariance is preserved with or without regularization
and therefore there is no Lorentz-Violating Chern-Simons term in QED.
