It would be legitimate to call the whole part the gluon [*dynamical*]{} or [*mechanical*]{} OAM.

Here, we want to make several important remarks on the above sum rules. First, our decomposition has a Lorentz-frame-independent meaning. This should be clear from the fact that the GPDs and PDFs appearing in our sum rules are manifestly Lorentz-invariant quantities. Recently, Goldman argued that the nucleon spin decomposition is frame-dependent [@Goldman11]. This is generally true. In fact, Leader recently proposed a sum rule for the transverse angular momentum [@Leader11]. In this sum rule, $P_0$, the energy of the nucleon, appears. It is clear that this sum rule is manifestly frame-dependent. Note, however, that our main interest here is the simplest and most fundamental longitudinal spin decomposition of the nucleon. We emphasize once again that the longitudinally spin decomposition is definitely frame-independent. We think it a welcome feature, since, then, the decomposition can be thought to reflect intrinsic properties of the nucleon, which are independent of the velocity which the nucleon is running with. Underlying reason why the longitudinal spin sum rule is Lorentz-frame independent seems very simple. The OAM component along the longitudinal direction comes from the motion in the perpendicular plane to this 