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

TL;DR

This paper demonstrates that proper evaluation of the effective Lagrangian in QED reveals short-distance interaction terms essential for gauge invariance, showing no Lorentz-violating Chern-Simons term exists when regularization is correctly handled.

Contribution

It clarifies the role of short-distance interaction terms in the effective Lagrangian and argues against the existence of Lorentz-violating Chern-Simons terms in QED when regularization is properly removed.

Findings

Short-distance interaction terms are essential for gauge invariance.

No Lorentz-violating Chern-Simons term exists in QED.

Proper evaluation restores gauge invariance without regularization.

Abstract

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.