Gauge invariant gluon spin operator for spinless non-linear wave solutions

TL;DR

This paper introduces a gauge-invariant gluon spin operator for non-linear wave solutions in SU(2) QCD, addressing the vanishing canonical spin density and proposing a new static monopole solution with finite energy density.

Contribution

It presents a novel gauge-invariant, Lorentz frame independent gluon spin density operator and a static Wu-Yang monopole solution with finite energy density in pure SU(2) QCD.

Findings

Finite energy density everywhere in the new solution

Presence of a mass scale parameter in solutions

Vanishing classical spin density in non-linear wave solutions

Abstract

We consider non-linear wave type solutions with mass scale parameter and vahished canonical spin density operator in a pure SU(2) quantum chtomodynamics (QCD). A new stationary solution which can be treated as a system of static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered non-linear wave type solutions have common features: presence of a mass scale parameter, non-vanishing projection of the color magnetic field along the propagation direction and zero spin density. The last property requires revision of the gauge invariant definition of the spin density operator which supposed to be massless vector field in the classical theory. We construct a gauge invariant definition of the classical gluon spin density which is unique and Lorentz frame independent.