Comment on "Does Gluons Carry Half of the Nucleon Momentum?" by X. S. Chen et. al. (PRL103, 062001 (2009))

TL;DR

This paper critiques a previous claim about a gauge-invariant definition of momentum in gauge theory, clarifying that the earlier result is based on a misunderstanding of gauge symmetry and is not physically valid.

Contribution

The paper provides a critical analysis showing that the proposed gauge-invariant momentum definition is not physically meaningful due to a misinterpretation of gauge symmetry.

Findings

The claimed gauge-invariant momentum is not physically valid.

The misunderstanding arises from generalizing Coulomb gauge results.

The critique clarifies the importance of proper gauge symmetry interpretation.

Abstract

The authors claim to have found a "proper", "gauge-invariant" definition of a charged-particle's momentum in gauge theory, which is more "superior" than the textbook version. I show that their result arises from a misunderstanding of gauge symmetry by generalizing the Coulomb gauge result indiscriminately and is not physical.