  Lorentz covariant and gauge invariant definitions of quark and gluon spin and
orbital angular momenta continue to pose a great theoretical challenge. A major
controversy on the fundamental concepts followed Chen et al proposal: the basic
idea is to split the gauge potential into pure gauge and physical components
motivated by the gauge symmetry. We term it gauge symmetry paradigm (GSP) to
distinguish it from the well-known inertial frame dependent
transverse-longitudinal decomposition (TLP). A thorough study adhering to the
traditional meaning of Lorentz covariance and gauge invariance is reported; it
leads to a new result: logically consistent development of GSP does not exist
and Chen et al proposal turns out to be either trivial or metamorphosed into
TLP. Going beyond the controversy and the spin sum rules the necessity for a
nonperurbative QCD approach to address the proton spin problem is underlined.
We suggest topological approach: generalized de Rham theorems for QCD, and spin
as a topological invariant for baryons are discussed. Nonabelian Stokes theorem
is applied to derive color flux for the closed loop in a variant of Burkardt's
U-shaped path. Similarity between Chen et al decomposition and Kondo
decomposition of the gauge potential is suggestive of a topological perspective
on the Chen et al proposal with interesting physics
