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

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.

9 pages, version accepted in Phys. Rev. D

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• Is gauge-invariant complete decomposition of the nucleon spin possible ?
• The light-front gauge-invariant energy-momentum tensor
• The Parton Orbital Angular Momentum: Status and Prospects
• Nucleon spin decomposition and differential geometry
• Gauge symmetry and background independence: Should the proton spin decomposition be path independent?
• Physical symmetries and gauge choices in the Landau problem
• Gauge Invariant Descriptions of Gluon Polarizations
• Gauge Invariant Descriptions of Gluon Polarizations Revisited
• Potential linear and angular momentum in the scalar diquark model
• On the decomposition theorem for gluons
• The contour gauge in use: telling untold
• Quark and gluon orbital angular momentum: Where are we?
• The gauge-invariant canonical energy-momentum tensor
• Spin structure of the nucleon on the light front
• The nucleon spin decomposition: news and experimental implications