Geometrical approach to the proton spin decomposition

TL;DR

This paper provides a detailed geometrical analysis of the gauge invariance and Lorentz covariance in the proton spin decomposition approach by Chen et al., clarifying theoretical aspects and addressing interpretational debates.

Contribution

It offers a geometrical perspective on gauge invariance and Lorentz covariance in the Chen et al. proton spin decomposition, clarifying the theoretical foundations and transformation laws involved.

Findings

Gauge invariance follows from a Stueckelberg-like mechanism.

Lorentz covariance is maintained with a suitable transformation law.

Debates are mainly about different physical interpretations.

Abstract

We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition. We show that the gauge invariance of this approach follows from a mechanism similar to the one used in the famous Stueckelberg trick. Stressing the fact that the Lorentz symmetry does not force the gauge potential to transform as a Lorentz four-vector, we show that the Chen et al. approach is Lorentz covariant provided that one uses the suitable Lorentz transformation law. We also make an attempt to summarize the present situation concerning the proton spin decomposition. We argue that the ongoing debates concern essentially the physical interpretation and are due to the plurality of the adopted pictures. We discuss these different pictures and propose a pragmatic point of view.