Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics

Abstract

The relativistic treatment of spin is a fundamental subject which has an old history. In various physical contexts it is necessary to separate the relativistic total angular momentum into an orbital and spin contribution. However, such decomposition is affected by ambiguities since one can always redefine the orbital and spin part through the so-called pseudo-gauge transformations. We analyze this problem in detail by discussing the most common choices of energy-momentum and spin tensors with an emphasis on their physical implications, and study the spin vector which is a pseudo-gauge invariant operator. We review the angular momentum decomposition as a crucial ingredient for the formulation of relativistic spin hydrodynamics and quantum kinetic theory with a focus on relativistic nuclear collisions, where spin physics has recently attracted significant attention. Furthermore, we point out the connection between pseudo-gauge transformations and the different definitions of the relativistic center of mass. Finally, we consider the Einstein-Cartan theory, an extension of conventional general relativity, which allows for a natural definition of the spin tensor.

Invited review for The European Physical Journal A, Topical Issue "Theory of Hot Matter and Relativistic Heavy-Ion Collisions (THOR)", 24 pages

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Cited by in corpus (58)

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• Dissipative Spin Dynamics in Relativistic Matter
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• From Kadanoff--Baym to Boltzmann equations for massive spin-1/2 fermions
• Ideal spin hydrodynamics from Wigner function approach
• Relativistic Spin Magnetohydrodynamics
• Spin polarization dynamics in the Gubser-expanding background
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• Relativistic dissipative spin hydrodynamics from kinetic theory with a nonlocal collision term
• Relativistic second-order spin hydrodynamics: an entropy-current analysis
• Theories of Relativistic Dissipative Fluid Dynamics
• Gyrohydrodynamics: Relativistic spinful fluid with strong vorticity
• Canonical and phenomenological formulations of spin hydrodynamics
• Pseudogauge dependence of the spin polarization and of the axial vortical effect
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• Spin Polarization Formula for Dirac Fermions at Local Equilibrium
• Effect of thermal shear on longitudinal spin polarization in a thermal model
• Spin relaxation rate for heavy quarks in weakly coupled QCD plasma
• Stability studies of first order spin-hydrodynamic frameworks
• Spin polarization dynamics in the non-boost-invariant background
• The causality and stability of relativistic spin-hydrodynamics
• Lorentz-covariant nonlocal collision term for spin-1/2 particles
• Damping of spin waves
• Relativistic hydrodynamics with spin in the presence of electromagnetic fields
• Pseudo-gauge dependence of quantum fluctuations of energy in a hot relativistic gas of fermions
• Boost invariant spin hydrodynamics within the first order in derivative expansion
• Pseudogauge freedom and the SO(3) algebra of spin operators
• Linear mode analysis from spin transport equation
• Spin waves in spin hydrodynamics
• Resummed spin hydrodynamics from quantum kinetic theory
• Cross effects in spin hydrodynamics: A revisit Entropy analysis and statistical operator
• An introduction to relativistic spin hydrodynamics
• Collisional corrections to spin polarization from quantum kinetic theory using Chapman-Enskog expansion
• Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD
• Quantum Kinetic Theory with Vector and Axial Gauge Fields
• Relativistic second-order spin hydrodynamics: A Kubo-type formulation for the quark-gluon plasma
• The spin alignment of vector mesons with light front quarks
• Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions
• Dynamical constraints on pseudo-gauge transformations
• Conserved and non-conserved Noether currents from the quantum effective action
• Chiral and deconfinement transitions in spin-polarized quark matter
• Chiral and deconfinement thermal transitions at finite quark spin polarization in lattice QCD simulations
• Pseudogauge ambiguity in the distributions of energy density, pressure, and shear force inside the nucleon
• Semi-Classical Spin Hydrodynamics in Flat and Curved Spacetime: Covariance, Linear Waves, and Bjorken Background
• Polarization in heavy ion collisions: a theoretical review
• Hybrid framework of Fermi-Dirac spin hydrodynamics
• On the non-uniqueness of the energy-momentum and spin currents
• Gradient corrections to the local-equilibrium energy-momentum tensor in the Zubarev approach
• Chiral restoration temperature at finite spin density in QCD
• Energy-momentum tensor form factors and spin density distribution in the nucleon calculated in a quantized Skyrme model with vector mesons
• Theoretical aspects of relativistic spin hydrodynamics coupled with electromagnetic fields
• Quantum statistical fluctuation of energy and its novel pseudo-gauge dependence
• Guiding center hydrodynamics with spin
• Chiral vortical conductivities and the moment of inertia of a rigidly rotating Fermi gas
• Perfect spinfluid: A divergence-type approach