Comment on "Spin and Orbital Angular Momentum in Gauge Theories" by X. S. Chen et. al. (PRL100, 232002 (2008))

TL;DR

This paper critically examines a proposed decomposition of angular momentum in gauge theories, highlighting fundamental issues with its mathematical consistency, gauge dependence, Lorentz properties, and physical measurability.

Contribution

It provides a detailed critique showing that the proposed angular momentum operators are non-local, gauge-dependent, and lack proper Lorentz transformation properties.

Findings

The operators do not satisfy canonical angular momentum commutation rules.

They are generally non-local in gauge theories.

They lack known physical measurement procedures.

Abstract

The individual parts of the total angular momentum operator in interacting theories cannot satisfy the canonical angular momentum commutation rule, including those proposed in the above paper. Furthermore, the operators in the new proposal a) are non-local in general gauge, b) do not have proper Lorentz transformation properties, and c) do not have any known physical measurements.