decomposition is another GIE based on the Coulomb gauge. (Concerning the idea of gauge-invariant extension (GIE), see also [@JXY12].) Their claim is that, since they are different GIEs, there is no reason to expect that they give the same physical predictions. However, it seems to us that their conclusion is heavily influenced by the following observation. That is, the explicit calculations of the evolution matrices for the momentum fractions of quarks and gluons by Chen et al. based on the generalized Coulomb gauge are advertized to give totally different answers from the standardly-believed ones, which the treatment in the light-cone gauge can reproduce as we shall see later. However, no one has checked the validity of their Coulomb gauge calculation yet. What would one conclude, if this discrepancy simply arises from some technical mistakes in the Coulomb gauge treatment of the problem ? We shall come back to this question at the end of sect. IV.

Next we turn to the decomposition (I) given in the form : $$M^{\mu \nu \lambda} \ = \ M^{\mu \nu \lambda}_{q-spin} \ + \ 
 M^{\mu \nu \lambda}_{q-OAM} \ + \ M^{\mu \nu \lambda}_{G-spin}
 \ + \ M^{\mu \nu \lambda}_{G-OAM} \ + \ M^{\mu \nu 