Relativistic hydrodynamics for spin-polarized fluids

Abstract

A R T I C L E I N F O Keywords: relativistic heavy-ion collisions relativistic hydrodynamics spin polarization pseudo-gauge transformations semi-classical expansion Pauli-Lubański vector A B S T R A C T Recent progress in the formulation of relativistic hydrodynamics for particles with spin one-half is reviewed. We start with general arguments advising introduction of a tensor spin chemical potential that plays a role of the Lagrange multiplier coupled to the spin angular momentum. Then, we turn to a discussion of spin-dependent distribution functions that have been recently proposed to construct a hydrodynamic framework including spin and serve as a tool in phenomenological studies of hadron polarization. Distribution functions of this type are subsequently used to construct the equilibrium Wigner functions that are employed in the semi-classical kinetic equation. The semi-classical expansion elucidates several aspects of the hydrodynamic approach, in particular, shows the ways in which different possible versions of hydrodynamics with spin can be connected by pseudo-gauge transformations. These results point out at using the de Grootvan Leeuwen -van Weert versions of the energy-momentum and spin tensors as the most natural and complete physical variables. Finally, a totally new method is proposed to design hydrodynamics with spin, which is based on the classical treatment of spin degrees of freedom. Interestingly, for small values of the spin chemical potential the new scheme brings the results that coincide with those obtained before. The classical approach also helps us to resolve problems connected with the normalization of the spin polarization three-vector. In addition, it clarifies the role of the Pauli-Lubański vector and the entropy current conservation. We close our review with several general comments presenting possible future developments of the discussed frameworks.

Zilch vortical effect, Berry phase, and kinetic theory

“…The CVE and ZVE of gauge fields may shed light on their contribution to the spin polarization of QGP and require further investigation. Finally, the Wigner function computed here may serve as a starting point to develop relativstic hydrodynamics with spin degrees of freedom for vector particles [76][77][78][79][80][81][82].…”

Unruh effect universality: emergent conical geometry from density operator

“…Various quantum-field effects associated with acceleration and vorticity have been discovered: the chiral vortical effect (CVE) [1][2][3][4][5], the Unruh effect [6], phase transitions due to rotation [7] and acceleration [8][9][10] of the medium. These effects are now also the subject of an experimental search in heavy ion collisions and quark-gluon plasma, in particular, vorticity, or more precisely the thermal vorticity tensor, can lead to polarization of hadrons [11][12][13][14], and acceleration is considered as a possible source of thermalization and hadronization [15,16].…”

Linear response theory and effective action of relativistic hydrodynamics with spin

“…This is a challenging problem even at an intuitive level because several characteristics associated with ideal fluids such as isotropy and conservation of circulation, will not apply when spin density is nonzero. Indeed, several approaches have been tried [1][2][3][4][5][6][7][8][9][10][11], with a consensus on even the fundamental dynamics still lacking.…”