Comment on "Noncommutative gauge theories and Lorentz symmetry, Phys. Rev. D {\bf 70}, 125004 (2004) by R.Banerjee, B.Chakraborty and K.Kumar"

TL;DR

This paper demonstrates that Lorentz symmetry is generally violated in noncommutative abelian gauge theories and provides a universal formula for the divergence of Noether currents, clarifying previous interpretations of Lorentz invariance.

Contribution

It introduces a general divergence formula for Noether currents that explains Lorentz symmetry violation in noncommutative gauge theories, unifying previous results under a broader framework.

Findings

Lorentz symmetry is generally absent in noncommutative abelian gauge theories.

A compact formula for the divergence of Noether currents is derived.

Previous claims of Lorentz invariance are shown to be specific cases of a broader violation.

Abstract

We show that Lorentz symmetry is generally absent for noncommutative (abelian) gauge theories and obtain a compact formula for the divergence of the Noether currents that allows a throughout study of this instance of symmetry violation. We use that formula to explain why the results of "Noncommutative gauge theories and Lorentz symmetry", Phys. Rev. D {\bf 70}, 125004 (2004) by R.Banerjee, B.Chakraborty and K.Kumar, interpreted there as new criteria for Lorentz {\it invariance}, are in fact just a particular case of the general expression for Lorentz {\it violation} obtained here. Finally, it is suggested that the divergence-formula should hold in a vast class of cases, such as, for instance, the Standard Model Extension.