Nucleon spin decomposition and differential geometry

TL;DR

This paper offers a differential geometric perspective on the Chen et al. nucleon spin decomposition, clarifying its relation to the dressing field method and challenging its claimed gauge invariance.

Contribution

It provides a genuine differential geometric understanding of the Chen et al. approach and clarifies its relation to the dressing field method.

Findings

The gauge invariance of the Chen et al. decomposition is actually unreal.

A geometric interpretation of the nucleon spin decomposition is proposed.

The relation to the dressing field method is elucidated.

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. Fran\c{c}ois, 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.