Canonical and phenomenological formulations of spin hydrodynamics

Abstract

Two formulations of relativistic hydrodynamics of particles with spin 1/2 are compared. The first approach, dubbed the canonical one, uses expressions for the energy-momentum and spin tensors that have properties that follow a direct application of Noether's theorem, which yields a totally antisymmetric spin tensor. The other one is based on a simplified form of the spin tensor and is commonly used in the current literature under the name of a phenomenological approach. We show that these two frameworks are equivalent, i.e., they can be directly connected by a suitably defined pseudogauge transformation, only if the first framework is initially improved by a suitable modification of the energy-momentum tensor (addition of a divergence-free term that cannot be interpreted as a pseudogauge). Our analysis uses arguments related to the positivity of entropy production. The latter turns out to be equivalent for the improved canonical and phenomenological frameworks.

arXiv commentPublished in Physical Review C, journal reference: Phys. Rev. C 108, 024902 (2023). This manuscript matches the published version. 12 pages with no figures

References in corpus (43)

• Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid
• Global polarization of $\Lambda$ hyperons in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• New theories of relativistic hydrodynamics in the LHC era
• Relativistic fluid dynamics with spin
• Polarization of $\Lambda$ ($\bar{\Lambda }$) hyperons along the beam direction in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Relativistic hydrodynamics for spin-polarized fluids
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Evidence of spin-orbital angular momentum interactions in relativistic heavy-ion collisions
• Generating spin polarization from vorticity through nonlocal collisions
• Relativistic dissipative spin dynamics in the relaxation time approximation
• Spin Hydrodynamics and Symmetric Energy-Momentum Tensors -- A current induced by the spin vorticity --
• Spin tensor and its role in non-equilibrium thermodynamics
• Hydrodynamics of spin currents
• Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation
• Global polarization of $\Lambda$ and $\overline{\Lambda }$ hyperons in Pb-Pb collisions at the LHC
• Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics
• From Chiral Kinetic Theory To Relativistic Viscous Spin Hydrodynamics
• The ideal relativistic fluid limit for a medium with polarization
• Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles
• Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory
• Global polarization of $\Xi$ and $\Omega$ hyperons in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Dissipative Spin Dynamics in Relativistic Matter
• Thermodynamic versus kinetic approach to polarization-vorticity coupling
• The ideal relativistic spinning gas: polarization and spectra
• The ideal relativistic rotating gas as a perfect fluid with spin
• Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics
• From Kadanoff--Baym to Boltzmann equations for massive spin-1/2 fermions
• Spin polarization evolution in a boost invariant hydrodynamical background
• Linear response theory of relativistic hydrodynamics with spin
• Causality and dissipation in relativistic polarizeable fluids
• Ideal spin hydrodynamics from Wigner function approach
• Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids
• Relativistic Viscous Hydrodynamics with Angular Momentum
• Sound waves and vortices in a polarized relativistic fluid
• Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion
• Relativistic second-order spin hydrodynamics: an entropy-current analysis
• Holographic spin liquids and Lovelock Chern-Simons gravity
• Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors
• Pseudogauge dependence of the spin polarization and of the axial vortical effect
• Stability studies of first order spin-hydrodynamic frameworks
• Kubo formulae for first-order spin hydrodynamics
• Boost invariant spin hydrodynamics within the first order in derivative expansion
• Cross effects in spin hydrodynamics: A revisit Entropy analysis and statistical operator

Cited by in corpus (20)

• Theories of Relativistic Dissipative Fluid Dynamics
• New developments in relativistic magnetohydrodynamics
• Damping of spin waves
• Hybrid approach to perfect and dissipative spin hydrodynamics
• Resummed spin hydrodynamics from quantum kinetic theory
• Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions
• An introduction to relativistic spin hydrodynamics
• Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD
• Boost-invariant spin hydrodynamics with spin feedback effects
• Effect of Coriolis Force on Electrical Conductivity Tensor for Rotating Hadron Resonance Gas
• Relativistic second-order spin hydrodynamics: A Kubo-type formulation for the quark-gluon plasma
• Effect of the Coriolis force on the electrical conductivity of quark matter: A nonrelativistic description
• Effect of Coriolis force on the shear viscosity of quark matter: A nonrelativistic description
• Spin Polarization of $\Lambda$ hyperons from Dissipative Spin Hydrodynamics
• Spin hydrodynamics -- recent developments
• Semi-Classical Spin Hydrodynamics in Flat and Curved Spacetime: Covariance, Linear Waves, and Bjorken Background
• Hybrid framework of Fermi-Dirac spin hydrodynamics
• Minimal-Length Corrections to Hyperon Polarization in Rotating Quark Gluon Plasma
• Guiding center hydrodynamics with spin
• On the local thermodynamic relations in relativistic spin hydrodynamics