Lorentz covariance and gauge invariance in the proton spin problem

TL;DR

This paper discusses the fundamental conflict between Lorentz covariance and gauge invariance in decomposing the proton's spin, highlighting that no single decomposition can satisfy both principles simultaneously and suggesting a need for fresh analysis of field equations.

Contribution

It clarifies the core conceptual issue in the proton spin decomposition controversy, emphasizing the incompatibility of Lorentz covariance and gauge invariance.

Findings

No decomposition satisfies both Lorentz covariance and gauge invariance simultaneously.

Partial approaches may conceal underlying inconsistencies.

A new analysis of field equations is necessary for progress.

Abstract

In this brief note insightful remarks are made on the controversy on the decomposition of the proton spin into the spin and orbital angular momenta of quarks and gluons. It is argued that the difference in the perception on the nature of the problem is the main reason for the persistent disputes. There is no decomposition that simultaneously satisfies the twin principles of manifest Lorentz covariance and gauge invariance, and partial considerations hide likely inconsistencies. It is suggested that field equations and matter (i. e. electron in QED and quarks in QCD) equations must be analyzed afresh rather than beginning with the expressions of total angular momentum; canonical or otherwise.