Induced Lorentz-Violating Chern-Simons Term in QED: Uncovering Short Distance Interaction Terms in the Effective Lagrangian without the Shadow of Regularization
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.