Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited

TL;DR

This paper resolves the gauge-invariance issue in nucleon spin structure by constructing explicit gauge-invariant angular momentum operators, enhancing understanding of nucleon spin and multipole radiation in gauge theories.

Contribution

It introduces explicit gauge-invariant operators for quark and gluon angular momentum, addressing a long-standing problem and clarifying the use of canonical operators in multipole radiation.

Findings

Gauge-invariant nucleon spin operators constructed

Justification of canonical operators in multipole analysis

Insights into energy-momentum in gauge theories

Abstract

We address and solve the long-standing gauge-invariance problem of the nucleon spin structure. Explicitly gauge-invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an impossible task, and opens a more promising avenue towards the understanding of the nucleon spin. Our research also justifies the traditional use of the canonical, gauge-dependent angular momentum operators of photons and electrons in the multipole-radiation analysis and labeling of atomic states; and sheds much light on the related energy-momentum problem in gauge theories, especially in connection with the nucleon momentum.