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Over recent years we have witnessed tremendous progresses in ourunderstanding on the angular momentum decomposition. In the context of theproton spin problem in high energy processes the angular momentum decompositionby Jaffe and Manohar, which is based on the canonical definition, and thealternative by Ji, which is based on the Belinfante improved one, have beenrevisited under light shed by Chen et al. leading to seminal works by Hatta,Wakamatsu, Leader, etc. In chiral physics as exemplified by the chiral vorticaleffect and applications to the relativistic nucleus-nucleus collisions,sometimes referred to as a relativistic extension of the Barnett and theEinstein--de Haas effects, such arguments of the angular momentum decompositionwould be of crucial importance. We pay our special attention to the fermionicpart in the canonical and the Belinfante conventions and discuss a differencebetween them, which is reminiscent of a classical example of Feynman's angularmomentum paradox. We point out its possible relevance to early-time dynamics inthe nucleus-nucleus collisions, resulting in excess by the electromagneticangular momentum.

Relativistic decomposition of the orbital and the spin angular momentum in chiral physics and Feynman's angular momentum paradox