The application of gauge invariance and canonical quantization to the internal structure of gauge field systems

TL;DR

This paper proposes a new decomposition of quark and gluon operators that satisfies both gauge invariance and canonical commutation relations, addressing a fundamental conflict in nucleon internal structure studies.

Contribution

A novel set of gauge-invariant and canonically commutable quark and gluon operators is introduced by separating gauge fields into pure gauge and covariant parts.

Findings

New operators satisfy both gauge invariance and canonical commutation relations.

Impacts on understanding nucleon internal structure are discussed.

Method applicable to QED and quantum mechanics.

Abstract

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However, we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.