Gauge symmetry and background independence: Should the proton spin decomposition be path independent?

TL;DR

This paper examines different gauge symmetry approaches to proton spin decomposition, highlighting the roles of path dependence, background dependence, and their physical measurability.

Contribution

It offers an alternative perspective connecting the Chen et al. approach with the background field method, clarifying the physical significance of various decompositions.

Findings

Path/Stueckelberg/background-dependent decompositions are measurable.

Gauge symmetry can be realized in two distinct ways.

Relations between path dependence, Stueckelberg dependence, and background dependence are clarified.

Abstract

Exploring the similarities between the Chen \emph{et al.} approach, where physical and gauge degrees of freedom of the gauge potential are explicitly separated, and the background field method, we provide an alternative point of view to the proton spin decomposition issue. We show in particular that the gauge symmetry can be realized in two different ways, and discuss the relations between the concepts of path dependence, Stueckelberg dependence and background dependence. Finally, we argue that path/Stueckelberg/background-dependent decompositions of the proton spin are in principle measurable and therefore physically meaningful.