The proton spin decomposition : path dependence and gauge symmetry

TL;DR

This paper examines various methods of decomposing the proton spin, emphasizing the measurability of certain approaches despite their non-uniqueness, and clarifies how gauge transformations influence these decompositions.

Contribution

It clarifies the role of gauge transformations in proton spin decompositions, resolving controversies and highlighting the measurability of Chen et al. and Wakamatsu methods.

Findings

Chen et al. and Wakamatsu decompositions are measurable.

Two types of gauge transformations are identified in the Chen et al. approach.

Understanding gauge transformations clarifies the concepts of gauge invariance and path dependence.

Abstract

We discuss the different types of decomposition of the proton spin. We stress that, despite their lack of uniqueness, the Chen et al. and Wakamatsu decompositions are perfectly measurable. We argue that a large part of the recent controversies boils down to the fact that there actually exist two types of gauge transformations in the Chen et al. approach, where physical and gauge degrees of freedom of the gauge potential are explicitly separated. By carefully distinguishing these two types of gauge transformations, one can easily understand how the concepts of gauge invariance, Stueckelberg symmetry, path dependence and measurability are linked to each other.