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

TL;DR

This paper explores the decomposition of orbital and spin angular momentum in relativistic and chiral physics, highlighting differences between canonical and Belinfante definitions and their implications for nuclear collision dynamics.

Contribution

It provides a detailed analysis of angular momentum decomposition in relativistic chiral physics, emphasizing the fermionic contributions and their relation to Feynman's angular momentum paradox.

Findings

Difference between canonical and Belinfante angular momentum decompositions highlighted.

Relevance of angular momentum decomposition to early-time dynamics in nucleus-nucleus collisions.

Potential excess electromagnetic angular momentum in high-energy nuclear interactions.

Abstract

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.