  Over recent years we have witnessed tremendous progresses in our
understanding on the angular momentum decomposition. In the context of the
proton spin problem in high energy processes the angular momentum decomposition
by Jaffe and Manohar, which is based on the canonical definition, and the
alternative by Ji, which is based on the Belinfante improved one, have been
revisited under light shed by Chen et al. leading to seminal works by Hatta,
Wakamatsu, Leader, etc. In chiral physics as exemplified by the chiral vortical
effect and applications to the relativistic nucleus-nucleus collisions,
sometimes referred to as a relativistic extension of the Barnett and the
Einstein--de Haas effects, such arguments of the angular momentum decomposition
would be of crucial importance. We pay our special attention to the fermionic
part in the canonical and the Belinfante conventions and discuss a difference
between them, which is reminiscent of a classical example of Feynman's angular
momentum paradox. We point out its possible relevance to early-time dynamics in
the nucleus-nucleus collisions, resulting in excess by the electromagnetic
angular momentum.
