Gauge-covariant canonical formalism revisited with application to the proton spin decomposition

TL;DR

This paper revisits the gauge-covariant canonical formalism, clarifying the derivation of gauge-invariant momentum operators and establishing their equivalence with Dirac variable-based approaches, with implications for gauge theories and gravity.

Contribution

It demonstrates the consistency of gauge-invariant momentum operators derived from Noether's theorem and links the formalism to Dirac variables, enhancing understanding of gauge symmetry in field theories.

Findings

Gauge-invariant operators derived from Noether's theorem are consistent.

The formalism is equivalent to the Dirac variable approach.

Potential applications to gravity and metric theories.

Abstract

We revisit the gauge-covariant canonical formalism by separating explicitly physical and gauge degrees of freedom. We show in particular that the gauge-invariant linear and angular momentum operators proposed by Chen et al. can consistently be derived from the standard procedure based on the Noether's theorem. Finally, we demonstrate that this approach is essentially equivalent to the gauge-invariant canonical formalism based on the concept of Dirac variables. Because of many similarities with the background field method, the formalism developed here should also be relevant to general relativity and any metric theories.