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The question whether the total gluon angular momentum in the nucleon can bedecomposed into its spin and orbital parts without conflict with thegauge-invariance principle has been an object of long-lasting debate. Despite aremarkable progress achieved through the recent intensive researches, thefollowing two issues still remains to be clarified more transparently. Thefirst issue is to resolve the apparent conflict between the proposedgauge-invariant decomposition of the total gluon angular momentum and thetextbook statement that the total angular momentum of the photon cannot begauge-invariantly decomposed into its spin and orbital parts. We show that thisproblem is also inseparably connected with the uniqueness or non-uniquenessproblem of the nucleon spin decomposition. The second practically moreimportant issue is that, among the two physically inequivalent decompositionsof the nucleon spin, i.e. the "canonical" type decomposition and the"mechanical" type decomposition, which can we say is more physical or closer todirect observation ? In the present paper, we try to answer both thesequestions as clearly as possible.

On the two remaning issues in the gauge-invariant decomposition problem of the nucleon spin