Abstract
Over recent years we have witnessed tremendous progress in our understanding of 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.
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Notes
- 1.
The spin identification in such a frame to drop spatial derivatives is emphasized by Yoshimasa Hidaka. Another physical constraint is the commutation relation, and this prescription would always give the correct commutation relation of the spin.
- 2.
K. F. thanks Wojciech Florkowski and Hidetoshi Taya for simulating conversations on this point which seem not to be very consistent to each other, and thus we just refer to their review and original literature here.
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Fukushima, K., Pu, S. (2021). Relativistic Decomposition of the Orbital and the Spin Angular Momentum in Chiral Physics and Feynman’s Angular Momentum Paradox. In: Becattini, F., Liao, J., Lisa, M. (eds) Strongly Interacting Matter under Rotation. Lecture Notes in Physics, vol 987. Springer, Cham. https://doi.org/10.1007/978-3-030-71427-7_12
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