  We discuss the uniqueness or non-uniqueness problem of the decomposition of
the gluon field into the physical and pure-gauge components, which is the basis
of the recently proposed two physically inequivalent gauge-invariant
decompositions of the nucleon spin. It is crucialy important to recognize the
fact that the standard gauge fixing procedure is essentially a process of
projecting out the physical components of the massless gauge field. A
complexity of the nonabelian gauge theory as compared with the abelian case is
that a closed expression for the physical component can be given only with use
of the non-local Wilson line, which is generally path-dependent. It is known
that, by choosing an infinitely long straight-line path in space and time, the
direction of which is characterized by a constant 4-vector $n^\mu$, one can
cover a class of gauge called the general axial gauge, containing three popular
gauges, i.e. the temporal, the light-cone, and the spatial axial gauge. Within
this general axial gauge, we have calculated the 1-loop evolution matrix for
the quark and gluon longitudinal spins in the nucleon. We found that the final
answer is exactly the same independently of the choices of $n^\mu$, which
amounts to proving the gauge-independence and path-independence simultaneously,
although within a restricted class of gauges and paths. By drawing on all of
these findings together with well-established knowledge from gauge theories, we
argue against the rapidly spreading view in the community that there are
infinitely many decompositions of the nucleon spin.
