Nucleon spin decomposition and differential geometry

In the past few years, the so-called Chen et al. approach of the nucleon spin decomposition has been widely discussed and elaborated on. In this article we propose a genuine differential geometric understanding of this approach. We mainly highlight its relation to the "dressing field method" we advocated in Fournel et al. [Int. J. Geom. Methods Mod. Phys. 11, 1450016 (2014)]. The gauge invariance of the Chen et al. decomposition is discussed.