Wilson lines and orbital angular momentum

TL;DR

This paper provides a detailed realization of proton spin decomposition using Wilson lines, clarifying gauge invariance and residual gauge freedom, and analyzing the equivalence of different orbital angular momentum definitions.

Contribution

It introduces a generalized approach to proton spin decomposition with explicit Wilson line constructions and examines gauge invariance and operator equivalences in this context.

Findings

Kinetic orbital angular momentum expressed via Wigner operator after momentum integration

Equivalence of light-front canonical orbital angular momenta (advanced, retarded, antisymmetric)

Clarification of residual gauge freedom in Wilson line formulations

Abstract

We present an explicit realization of the Chen et al. approach to the proton spin decomposition in terms of Wilson lines, generalizing the light-front gauge-invariant extensions discussed recently by Hatta. Particular attention is drawn to the residual gauge freedom by further separating the pure-gauge term into contour and residual terms. We show that the kinetic orbital angular momentum operator can be expressed in terms of the Wigner operator only when the momentum variable is integrated over. Finally, we confirm from twist-2 arguments that the advanced, retarded and antisymmetric light-front canonical orbital angular momenta are the same.