Gauge- and frame-independent decomposition of nucleon spin

In a recent paper, we have shown that the way of gauge-invariant decomposition of the nucleon spin is not necessarily unique, but there still exists a preferable decomposition from the observational viewpoint. What was not complete in this argument is a fully satisfactory answer to the following questions. Does the proposed gauge-invariant decomposition, especially the decomposition of the gluon total angular momentum into its spin and orbital parts, correspond to observables which can be extracted from high-energy deep-inelastic-scattering measurements ? Is this decomposition not only gauge invariant but also Lorentz frame independent, so that it is legitimately thought to reflect an intrinsic property of the nucleon? We show that we can answer both of these questions affirmatively by making full use of a gauge-invariant decomposition of the covariant angular-momentum tensor of QCD in an arbitrary Lorentz frame.