Nucleon spin decomposition and differential geometry

Abstract

In the last few years, the so-called Chen et al. approach of the nucleon spin decomposition has been widely discussed and elaborated on. In this letter we propose a genuine differential geometric understanding of this approach. We mainly highligth its relation to the "dressing field method" we advocated in [C. Fournel, J. François, S. Lazzarini, T. Masson, Int. J. Geom. Methods Mod. Phys. 11, 1450016 (2014)]. We are led to the conclusion that the claimed gauge-invariance of the Chen et al. decomposition is actually unreal.

9 pages. v3: minor corrections in the text, addition of a new reference

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• Weyl gravity and Cartan geometry
• The dressing field method of gauge symmetry reduction, a review with examples
• Tractors and Twistors from conformal Cartan geometry: a gauge theoretic approach I. Tractors
• Tractors and Twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors
• BRST structure for the mixed Weyl-diffeomorphism residual symmetry
• On the canonical formulation of gauge field theories and Poincare transformations
• On the two remaning issues in the gauge-invariant decomposition problem of the nucleon spin
• Unconventional Supersymmetry via the Dressing Field Method
• Relational Supersymmetry via the Dressing Field Method and Matter-Interaction Supergeometric Framework