  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 covariant angular momentum tensor of QCD in an
arbitrary Lorentz frame.
