  Is gauge-invariant complete decomposition of the nucleon spin possible?
Although it is a difficult theoretical question which has not reached a
complete consensus yet, a general agreement now is that there are at least two
physically inequivalent gauge-invariant decompositions (I) and (II) of the
nucleon. %The one is a nontrivial gauge-invariant %generalization of the
Jaffe-Manohar decomposition. %The other is an extension of the Ji
decomposition, which allows %a gauge-invariant decomposition of the total gluon
angular %momentum into the intrinsic spin and orbital parts. In these two
decompositions, the intrinsic spin parts of quarks and gluons are just common.
What discriminate these two decompositions are the orbital angular momentum
parts. The orbital angular momenta of quarks and gluons appearing in the
decomposition (I) are the so-called "mechanical" orbital angular momenta, while
those appearing in the decomposition (II) are the generalized (gauge-invariant)
"canonical" ones. By this reason, these decompositions are also called the
"mechanical" and "canonical" decompositions of the nucleon spin, respectively.
A crucially important question is which decomposition is more favorable from
the observational viewpoint. The main objective of this concise review is to
try to answer this question with careful consideration of recent intensive
researches on this problem.
