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

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. PrologueSome time ago we, Fukushima and Pu, together with our bright colleague, Zebin Qiu, published a paper [1] on a relativistic extension of the Barnett effect [2] in the context of chiral materials. Our results are beautiful and robust, we believe, but at the same time, we had to overcome many conceptual confusions. We are

Effective quantum kinetic theory for spin transport of fermions with collsional effects

“…Such a derivation is more explicitly shown in the review paper [77] (See also Ref. [78]). Here we just summarize the derivation therein.…”

Foundations and Applications of Quantum Kinetic Theory

“…that keeps J µν invariant. One can find more detailed discussion in recent reviews [89,307] and related works for dissipative spin hydrodynamics [306,308,309,329,320].…”

“…The relativistic spin hydrodynamics is a macroscopic theory for tracking the evolution of spin degrees of freedom, in which the conservation equation of angular momentum is added to those of energy-momentum and conserved charges in conventional hydrodynamics. The spin hydrodynamics can be constructed from the entropy principle [306,307,308,309,310], the effective Lagrangian theory [311,312], kinetic approaches [313,314,315,175,316,317], and quantum field theory [318,319,320]. The ideal spin hydrodynamics can be constructed from spin-dependent distribution functions [321,313] with further applications [322,314,323,324,318,316], see Ref.…”

“…With a gradient expansion, the dissipative spin hydrodynamics can be derived in a canonical [306,325,326,317,320] and a Belinfante form [307,308]. The spin hydrodynamics has also been applied to background expanding systems [323,327,328] and analytic solutions can be found in a Bjorken flow [329] and Gubser flow [330].…”

Strongly Interacting Matter Under Rotation: An Introduction

“…More broadly, the presence of global rotation has opened a new dimension for investigating its nontrivial effects, for example, on the phase structures of matter (see chapter 11 [29]) or on the interplay between orbital and spin angular momentum (c.f. chapter 12 [30]).…”