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

Abstract: The question whether the total gluon angular momentum in the nucleon can be decomposed into its spin and orbital parts without conflict with the gauge-invariance principle has been an object of long-lasting debate. Despite a remarkable progress achieved through the recent intensive researches, the following two issues still remains to be clarified more transparently. The first issue is to resolve the apparent conflict between the proposed gauge-invariant decomposition of the total gluon angular momentum and the textbook statement that the total angular momentum of the photon cannot be gauge-invariantly decomposed into its spin and orbital parts. We show that this problem is also inseparably connected with the uniqueness or non-uniqueness problem of the nucleon spin decomposition. The second practically more important issue is that, among the two physically inequivalent decompositions of the nucleon spin, i.e. the "canonical" type decomposition and the "mechanical" type decomposition, which can we say is more physical or closer to direct observation ? In the present paper, we try to answer both these questions as clearly as possible.