Gauge invariance, Lorentz covariance and canonical quantization in nucleon structure studies

TL;DR

This paper examines the definitions of quark and gluon momentum, angular momentum, and spin operators in nucleon structure, emphasizing gauge invariance, Lorentz covariance, and canonical quantization to propose a gauge-invariant decomposition.

Contribution

It introduces a gauge-invariant canonical decomposition of nucleon momentum and angular momentum based on splitting gauge potentials into physical and pure gauge parts.

Findings

Analyzed advantages and disadvantages of different operator definitions.

Proposed a gauge-invariant decomposition of total momentum and angular momentum.

Addressed challenges to the gauge-invariant decomposition proposal.

Abstract

There are different operators of quark and gluon momenta, orbital angular momenta, and gluon spin in the nucleon structure study. The precise meaning of these operators are studied based on gauge invariance, Lorentz covariance and canonical quantization rule. The advantage and disadvantage of different definitions are analyzed. A gauge invariant canonical decomposition of the total momentum and angular momentum into quark and gluon parts is suggested based on the decomposition of the gauge potential into gauge invariant (covariant) physical part and gauge dependent pure gauge part. Challenges to this proposal are answered. \keywords{Physical and pure gauge potentials; Gauge invariant canonical quark and gluon momenta, orbital angular momenta and spins; Homogeneous and non-homogeneous Lorentz transformations; Gauge invariant decomposition and gauge invariant extension; Classical and quantum measurements.