importance to make clear why there exist two decompositions at all and in what essential respects they are different. One of the purposes of the present paper is to clarify the physical meaning of this potential angular momentum term in a clearest fashion with the help of a plainer example from electrodynamics, i.e. through an analysis of a system of charged particles and photons, analogous to a system of color-charged quarks and gluons.

We also try to clarify several other issues left in the decomposition problem of the nucleon spin momentum. It is known that there also exist two different gauge-invariant decompositions of the nucleon momentum into the contributions of quarks and gluons. On the basis of a gauge-invariant decomposition of the nucleon momentum, which is different from the standardly-known one, Chen et al. threw doubt on a common wisdom of deep-inelastic-scattering physics that the gluons carry about half of the nucleon momentum in the asymptotic limit [@Chen09]. To verify the validity of this claim is of fundamental importance, since it challenges our common knowledge on one of the basics of perturbative QCD.

Also important to understand is a puzzling observation on the scale dependencies of the quark and gluon 