pith. machine review for the scientific record. sign in

arxiv: 2605.12554 · v1 · submitted 2026-05-11 · ⚛️ nucl-th · hep-ph· hep-th

Recognition: 2 theorem links

· Lean Theorem

Spin dynamics and polarization in relativistic systems: recent developments

Amaresh Jaiswal, Arpan Das, Hiranmaya Mishra, Sourav Dey

Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:46 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phhep-th
keywords spin polarizationrelativistic hydrodynamicsheavy ion collisionsquark gluon plasmavorticitypseudo-gauge freedomspin dynamics
0
0 comments X

The pith

Pseudo-gauge freedom in tensor definitions affects predictions of spin polarization in relativistic heavy-ion collisions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review examines how spin polarization of hadrons emerges from vorticity in the quark-gluon plasma created during non-central heavy-ion collisions. It covers theoretical approaches including relativistic hydrodynamics, kinetic theory, and quantum statistical methods. Central to the discussion is the pseudo-gauge freedom, which allows different equivalent definitions of the energy-momentum and spin tensors and thereby influences calculated polarization observables. Understanding these effects is important for developing consistent models that can be compared with experimental measurements of polarization. The work also addresses spin hydrodynamics with gradient expansions and heavy flavor dynamics through rotational Brownian motion.

Core claim

The review establishes that the role of pseudo-gauge freedom has important implications for defining energy-momentum and spin tensors, which in turn can influence theoretical predictions of polarization observables in relativistic systems.

What carries the argument

Pseudo-gauge freedom, allowing multiple but equivalent ways to define the energy-momentum and spin tensors in relativistic theories.

If this is right

  • Different choices in pseudo-gauges lead to varying structures in spin hydrodynamics theories and their transport coefficients.
  • Spin chemical potential and entropy current analysis determine the form of the hydrodynamic equations for spin.
  • Polarization harmonics connect spin polarization to the initial geometry of the collision.
  • Rotational Brownian motion provides a framework for spin relaxation in heavy flavor particles under strong magnetic fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Resolving gauge ambiguities might require developing gauge-invariant observables for polarization.
  • Integrating these ideas with full dynamical simulations of heavy-ion collisions could yield more accurate predictions.
  • Experimental data on polarization could help discriminate between different theoretical formulations of spin hydrodynamics.

Load-bearing premise

The assumption that the body of cited work on spin hydrodynamics and pseudo-gauge transformations provides a coherent and complete foundation without internal contradictions.

What would settle it

Experimental observation of hadron polarization values that match predictions from one specific pseudo-gauge choice but deviate systematically from others would confirm or refute the influence of gauge freedom.

Figures

Figures reproduced from arXiv: 2605.12554 by Amaresh Jaiswal, Arpan Das, Hiranmaya Mishra, Sourav Dey.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison of the global Λ polarization measurements reported by STAR [ [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A schematic depiction of a non-central heavy-ion collision is shown, where the magnetic field [PITH_FULL_IMAGE:figures/full_fig_p037_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time evolution of the magnetic field and its modification due to the finite electrical conductivity of the QGP at top [PITH_FULL_IMAGE:figures/full_fig_p038_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Each point on the unit sphere corresponds to a distinct orientation of the heavy-quark spin vector. The evolution of [PITH_FULL_IMAGE:figures/full_fig_p041_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Schematic representation of heavy-quark spin dynamics in a quark–gluon plasma (QGP). Initially polarized heavy [PITH_FULL_IMAGE:figures/full_fig_p045_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The ALICE Collaboration results for the spin-alignment observable [PITH_FULL_IMAGE:figures/full_fig_p046_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Predictions for polarization of open-charmed baryons, expressed as [PITH_FULL_IMAGE:figures/full_fig_p047_7.png] view at source ↗
read the original abstract

We review recent theoretical and experimental developments in spin dynamics and polarization phenomena in relativistic systems, with a particular focus on heavy-ion collisions. The large angular momentum and magnetic field generated in non-central collisions induce vorticity in the quark-gluon plasma, leading to observable spin polarization of emitted hadrons. We discuss the theoretical foundations of spin polarization arising from spin-vorticity coupling, including formulations based on relativistic hydrodynamics, kinetic theory, and quantum statistical approaches such as the Zubarev density operator. A central theme of the review is the role of pseudo-gauge freedom and its implications for defining energy-momentum and spin tensors, which can influence theoretical predictions of polarization observables. We further examine different formulations of spin hydrodynamics, emphasizing the impact of gradient expansions, spin chemical potential, and entropy-current analysis on the structure of the theory and associated transport coefficients. In addition, we discuss the recent developments in heavy flavor spin dynamics within the framework of rotational Brownian motion, where spin degrees of freedom undergo stochastic evolution due to interactions with the medium. This framework provides a complementary perspective on spin relaxation and diffusion by incorporating the effects of strong initial magnetic fields and establishes connections between spin polarization and the initial geometry through the definition of polarization harmonics. This review provides a comprehensive overview of relativistic spin hydrodynamics as well as non-equilibrium spin dynamics, and outlines future directions toward a consistent and predictive description of spin phenomena in strongly interacting matter.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. This manuscript is a review of recent theoretical and experimental developments in spin dynamics and polarization in relativistic systems, with emphasis on heavy-ion collisions. It covers the generation of vorticity and magnetic fields leading to hadron spin polarization, theoretical foundations from relativistic hydrodynamics, kinetic theory, and the Zubarev density operator, the implications of pseudo-gauge freedom for energy-momentum and spin tensors, alternative formulations of spin hydrodynamics (gradient expansions, spin chemical potential, entropy current), heavy-flavor spin dynamics via rotational Brownian motion, and connections between polarization harmonics and initial geometry. The review concludes by outlining future directions for a consistent description of spin phenomena.

Significance. If the synthesis accurately reflects the cited literature, the review is significant for clarifying the conceptual role of pseudo-gauge freedom in polarization observables and for connecting hydrodynamic, kinetic, and stochastic approaches. It provides a broad overview that could help organize ongoing work in relativistic spin hydrodynamics and non-equilibrium dynamics, while highlighting links to experimental observables in heavy-ion collisions.

major comments (1)
  1. The central claim that different formulations (Zubarev operator, gradient expansions, spin chemical potential) can be treated as complementary rests on the assumption that pseudo-gauge choices do not produce inequivalent observables; this point is load-bearing for the review's coherence but receives only descriptive treatment without an explicit comparison of predicted polarization signals across choices.
minor comments (2)
  1. The abstract and introduction would benefit from a short table or bullet list enumerating the main formulations discussed and their key transport coefficients to improve readability for non-specialists.
  2. Ensure that all cited experimental results on polarization harmonics are accompanied by the specific collision systems and energies referenced, to allow direct connection to the theoretical sections.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the review's scope and significance. We address the single major comment below and will incorporate the suggested clarification in the revised manuscript.

read point-by-point responses

  1. Referee: The central claim that different formulations (Zubarev operator, gradient expansions, spin chemical potential) can be treated as complementary rests on the assumption that pseudo-gauge choices do not produce inequivalent observables; this point is load-bearing for the review's coherence but receives only descriptive treatment without an explicit comparison of predicted polarization signals across choices.

    Authors: We agree that the manuscript would benefit from a more explicit discussion of how pseudo-gauge choices affect (or do not affect) predicted polarization observables. While the review synthesizes the existing literature rather than performing new calculations, we will add a concise paragraph in the section on pseudo-gauge freedom that summarizes the current status of comparisons between formulations, cites the key works where partial equivalences or differences have been examined, and notes that full equivalence of observables remains an active research topic. This addition will clarify the basis for treating the approaches as complementary without overstating the current level of consensus. revision: yes

Circularity Check

0 steps flagged

Review synthesis of spin hydrodynamics shows no significant circularity

full rationale

This is a review paper that synthesizes existing literature on spin dynamics, polarization, pseudo-gauge freedom, and spin hydrodynamics in relativistic systems without advancing new derivations, quantitative predictions, or fitted parameters. The abstract and structure present alternative formulations (Zubarev operator, gradient expansions, spin chemical potential) as complementary perspectives drawn from cited external works in hydrodynamics and kinetic theory. No load-bearing steps reduce by construction to self-referential inputs, author-overlapping uniqueness theorems, or ansatzes smuggled via self-citation; the central theme is a survey of implications rather than a forced equivalence. Minor self-citations are expected in a review but do not bear the load of any claimed result, keeping the overall circularity low.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review article, the paper does not introduce new free parameters, axioms, or invented entities; it discusses existing frameworks from the cited literature on relativistic hydrodynamics and spin dynamics.

pith-pipeline@v0.9.0 · 5556 in / 1125 out tokens · 48338 ms · 2026-05-14T21:46:20.959072+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Reference graph

Works this paper leans on

262 extracted references · 262 canonical work pages · 96 internal anchors

  1. [1]

    Angular momentum conservation in heavy ion collisions at very high energy

    F. Becattini, F. Piccinini, and J. Rizzo, “Angular momentum conservation in heavy ion collisions at very high energy,” Phys. Rev.C77(2008) 024906,arXiv:0711.1253 [nucl-th]. [2]ST ARCollaboration, B. I. Abelevet al., “Global polarization measurement in Au+Au collisions,”Phys. Rev. C76 (2007) 024915,arXiv:0705.1691 [nucl-ex]. [Erratum: Phys.Rev.C 95, 039906 (2017)]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  2. [2]

    Magnetization by rotation,

    S. J. Barnett, “Magnetization by rotation,”Physical Review6(1915) 239–270. https://link.aps.org/doi/10.1103/PhysRev.6.239

    work page doi:10.1103/physrev.6.239 1915

  3. [3]

    Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid

    M. Takahashi, S. Murakami, N. Nagaosa, and Y. Tokura, “Spin hydrodynamic generation,”Nature Physics12(2016) 52–56.https://doi.org/10.1038/nphys3526. [5]ST ARCollaboration, L. Adamczyket al., “Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid,”Nature548(2017) 62–65,arXiv:1701.06657 [nucl-ex]. [6]ST ARCollaboration, J...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/nphys3526 2016

  4. [4]

    Study of Lambda polarization in relativistic nuclear collisions at sqrt{s}_NN = 7.7-200 GeV

    I. Karpenko and F. Becattini, “Study of Λ polarization in relativistic nuclear collisions at √sNN = 7.7 –200 GeV,”Eur. Phys. J.C77no. 4, (2017) 213,arXiv:1610.04717 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  5. [5]

    Global $\Lambda$ polarization in heavy-ion collisions from a transport model

    H. Li, L.-G. Pang, Q. Wang, and X.-L. Xia, “Global Λ polarization in heavy-ion collisions from a transport model,” Phys. Rev.C96no. 5, (2017) 054908,arXiv:1704.01507 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  6. [6]

    Is different Λ and ¯Λ polarization caused by different spatio-temporal freeze-out picture?,

    O. Vitiuk, L. V. Bravina, and E. E. Zabrodin, “Is different Λ and ¯Λ polarization caused by different spatio-temporal freeze-out picture?,”Phys. Lett. B803(2020) 135298,arXiv:1910.06292 [hep-ph]

    work page arXiv 2020

  7. [7]

    Lambda hyperon polarization in relativistic heavy ion collisions from the chiral kinetic approach

    Y. Sun and C. M. Ko, “Λ hyperon polarization in relativistic heavy ion collisions from a chiral kinetic approach,”Phys. Rev.C96no. 2, (2017) 024906,arXiv:1706.09467 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  8. [8]

    Polarization and Vorticity in the Quark–Gluon Plasma,

    F. Becattini and M. A. Lisa, “Polarization and Vorticity in the Quark–Gluon Plasma,”Ann. Rev. Nucl. Part. Sci.70 (2020) 395–423,arXiv:2003.03640 [nucl-ex]

    work page arXiv 2020

  9. [9]

    Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy

    F. Becattini and I. Karpenko, “Collective Longitudinal Polarization in Relativistic Heavy-Ion Collisions at Very High Energy,”Phys. Rev. Lett.120no. 1, (2018) 012302,arXiv:1707.07984 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  10. [10]

    Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP

    L. Del Zanna, V. Chandra, G. Inghirami, V. Rolando, A. Beraudo, A. De Pace, G. Pagliara, A. Drago, and F. Becattini, “Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP,”Eur. Phys. J. C73(2013) 2524, arXiv:1305.7052 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  11. [11]

    A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions

    I. Karpenko, P. Huovinen, and M. Bleicher, “A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions,”Comput. Phys. Commun.185(2014) 3016–3027,arXiv:1312.4160 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  12. [12]

    Estimates of hyperon polarization in heavy-ion collisions at collision energies √sN N = 4–40 GeV,

    Y. B. Ivanov, V. D. Toneev, and A. A. Soldatov, “Estimates of hyperon polarization in heavy-ion collisions at collision energies √sN N = 4–40 GeV,”Phys. Rev. C100no. 1, (2019) 014908,arXiv:1903.05455 [nucl-th]

    work page arXiv 2019

  13. [13]

    Spin Hall effect in heavy-ion collisions,

    S. Y. F. Liu and Y. Yin, “Spin Hall effect in heavy-ion collisions,”Phys. Rev. D104no. 5, (2021) 054043, arXiv:2006.12421 [nucl-th]

    work page arXiv 2021

  14. [14]

    Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions,

    C. Yi, S. Pu, and D.-L. Yang, “Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions,”Phys. Rev. C104no. 6, (2021) 064901,arXiv:2106.00238 [hep-ph]

    work page arXiv 2021

  15. [15]

    Evolution of Λ polarization in the hadronic phase of heavy-ion collisions,

    Y. Sun, Z. Zhang, C. M. Ko, and W. Zhao, “Evolution of Λ polarization in the hadronic phase of heavy-ion collisions,” Phys. Rev. C105no. 3, (2022) 034911,arXiv:2112.14410 [nucl-th]

    work page arXiv 2022

  16. [16]

    Effect of thermal shear on longitudinal spin polarization in a thermal model,

    W. Florkowski, A. Kumar, A. Mazeliauskas, and R. Ryblewski, “Effect of thermal shear on longitudinal spin polarization in a thermal model,”Phys. Rev. C105no. 6, (2022) 064901,arXiv:2112.02799 [hep-ph]

    work page arXiv 2022

  17. [17]

    Nonlinear Responses of Chiral Fluids from Kinetic Theory

    Y. Hidaka, S. Pu, and D.-L. Yang, “Nonlinear Responses of Chiral Fluids from Kinetic Theory,”Phys. Rev.D97no. 1, (2018) 016004,arXiv:1710.00278 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    Spin and polarization: a new direction in relativistic heavy ion physics,

    F. Becattini, “Spin and polarization: a new direction in relativistic heavy ion physics,”Rept. Prog. Phys.85no. 12, (2022) 122301,arXiv:2204.01144 [nucl-th]

    work page arXiv 2022

  19. [19]

    Recent developments in chiral and spin polarization effects in heavy-ion collisions,

    J.-H. Gao, G.-L. Ma, S. Pu, and Q. Wang, “Recent developments in chiral and spin polarization effects in heavy-ion collisions,”Nucl. Sci. Tech.31no. 9, (2020) 90,arXiv:2005.10432 [hep-ph]

    work page arXiv 2020

  20. [20]

    Polarization in relativistic fluids: a quantum field theoretical derivation,

    F. Becattini, “Polarization in relativistic fluids: a quantum field theoretical derivation,”Lect. Notes Phys.987(2021) 15–52,arXiv:2004.04050 [hep-th]

    work page arXiv 2021

  21. [21]

    Global and local spin polarization in heavy ion collisions: a brief overview

    Q. Wang, “Global and local spin polarization in heavy ion collisions: a brief overview,”Nucl. Phys. A967(2017) 225–232,arXiv:1704.04022 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  22. [22]

    Thermodynamic versus kinetic approach to polarization-vorticity coupling

    W. Florkowski, A. Kumar, and R. Ryblewski, “Thermodynamic versus kinetic approach to polarization-vorticity coupling,”Phys. Rev.C98(2018) 044906,arXiv:1806.02616 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  23. [23]

    Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles

    W. Florkowski, B. Friman, A. Jaiswal, R. Ryblewski, and E. Speranza, “Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles,”Phys. Rev.D97no. 11, (2018) 116017,arXiv:1712.07676 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  24. [24]

    Relativistic fluid dynamics with spin

    W. Florkowski, B. Friman, A. Jaiswal, and E. Speranza, “Relativistic fluid dynamics with spin,”Phys. Rev.C97no. 4, (2018) 041901,arXiv:1705.00587 [nucl-th]. 52

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  25. [25]

    Spin polarization evolution in a boost invariant hydrodynamical background

    W. Florkowski, A. Kumar, R. Ryblewski, and R. Singh, “Spin polarization evolution in a boost invariant hydrodynamical background,”Phys. Rev.C99no. 4, (2019) 044910,arXiv:1901.09655 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  26. [26]

    Longitudinal spin polarization in a thermal model,

    W. Florkowski, A. Kumar, R. Ryblewski, and A. Mazeliauskas, “Longitudinal spin polarization in a thermal model,” Phys. Rev.C100no. 5, (2019) 054907,arXiv:1904.00002 [nucl-th]

    work page arXiv 2019

  27. [27]

    Fate of spin polarization in a relativistic fluid: An entropy-current analysis

    K. Hattori, M. Hongo, X.-G. Huang, M. Matsuo, and H. Taya, “Fate of spin polarization in a relativistic fluid: An entropy-current analysis,”Phys. Lett.B795(2019) 100–106,arXiv:1901.06615 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  28. [28]

    Spin hydrodynamics and symmetric energy-momentum tensors – A current induced by the spin vorticity –,

    K. Fukushima and S. Pu, “Spin hydrodynamics and symmetric energy-momentum tensors – A current induced by the spin vorticity –,”Phys. Lett. B817(2021) 136346,arXiv:2010.01608 [hep-th]

    work page arXiv 2021

  29. [29]

    Nondissipative Second-Order Transport, Spin, and Pseudogauge Transformations in Hydrodynamics,

    S. Li, M. A. Stephanov, and H.-U. Yee, “Nondissipative Second-Order Transport, Spin, and Pseudogauge Transformations in Hydrodynamics,”Phys. Rev. Lett.127no. 8, (2021) 082302,arXiv:2011.12318 [hep-th]

    work page arXiv 2021

  30. [30]

    Relativistic viscous hydrodynamics with angular momentum,

    D. She, A. Huang, D. Hou, and J. Liao, “Relativistic viscous hydrodynamics with angular momentum,”Sci. Bull.67 (2022) 2265–2268,arXiv:2105.04060 [nucl-th]

    work page arXiv 2022

  31. [31]

    Sound waves and vortices in a polarized relativistic fluid

    D. Montenegro, L. Tinti, and G. Torrieri, “Sound waves and vortices in a polarized relativistic fluid,”Phys. Rev.D96 no. 7, (2017) 076016,arXiv:1703.03079 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  32. [32]

    The ideal relativistic fluid limit for a medium with polarization

    D. Montenegro, L. Tinti, and G. Torrieri, “The ideal relativistic fluid limit for a medium with polarization,”Phys. Rev. D96no. 5, (2017) 056012,arXiv:1701.08263 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  33. [33]

    Perfect-fluid hydrodynamics with constant acceleration along the stream lines and spin polarization

    W. Florkowski, E. Speranza, and F. Becattini, “Perfect-fluid hydrodynamics with constant acceleration along the stream lines and spin polarization,”Acta Phys. Polon.B49(2018) 1409,arXiv:1803.11098 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  34. [34]

    Relativistic dissipative spin dynamics in the relaxation time approximation,

    S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ryblewski, “Relativistic dissipative spin dynamics in the relaxation time approximation,”Phys. Lett. B814(2021) 136096,arXiv:2002.03937 [hep-ph]

    work page arXiv 2021

  35. [35]

    From Chiral Kinetic Theory To Spin Hydrodynamics,

    S. Shi, C. Gale, and S. Jeon, “From Chiral Kinetic Theory To Spin Hydrodynamics,”Nucl. Phys. A1005(2021) 121949,arXiv:2002.01911 [nucl-th]

    work page arXiv 2021

  36. [36]

    Relativistic second-order dissipative spin hydrodynamics from the method of moments,

    N. Weickgenannt, D. Wagner, E. Speranza, and D. H. Rischke, “Relativistic second-order dissipative spin hydrodynamics from the method of moments,”Phys. Rev. D106no. 9, (2022) 096014,arXiv:2203.04766 [nucl-th]

    work page arXiv 2022

  37. [37]

    Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism,

    N. Weickgenannt, X.-L. Sheng, E. Speranza, Q. Wang, and D. H. Rischke, “Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism,”arXiv:1902.06513 [hep-ph]

    work page arXiv 1902

  38. [38]

    Generating Spin Polarization from Vorticity through Nonlocal Collisions,

    N. Weickgenannt, E. Speranza, X.-l. Sheng, Q. Wang, and D. H. Rischke, “Generating Spin Polarization from Vorticity through Nonlocal Collisions,”Phys. Rev. Lett.127no. 5, (2021) 052301,arXiv:2005.01506 [hep-ph]

    work page arXiv 2021

  39. [39]

    Challenges in solving chiral hydrodynamics,

    E. Speranza, F. S. Bemfica, M. M. Disconzi, and J. Noronha, “Challenges in solving chiral hydrodynamics,”Phys. Rev. D107no. 5, (2023) 054029,arXiv:2104.02110 [hep-th]

    work page arXiv 2023

  40. [40]

    Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion,

    D.-L. Wang, S. Fang, and S. Pu, “Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion,”Phys. Rev. D104no. 11, (2021) 114043,arXiv:2107.11726 [nucl-th]

    work page arXiv 2021

  41. [41]

    Hydrodynamics of spin currents,

    A. D. Gallegos, U. G¨ ursoy, and A. Yarom, “Hydrodynamics of spin currents,”SciPost Phys.11(2021) 041, arXiv:2101.04759 [hep-th]

    work page arXiv 2021

  42. [42]

    From chiral kinetic theory to relativistic viscous spin hydrodynamics,

    S. Shi, C. Gale, and S. Jeon, “From chiral kinetic theory to relativistic viscous spin hydrodynamics,”Phys. Rev. C103 no. 4, (2021) 044906,arXiv:2008.08618 [nucl-th]

    work page arXiv 2021

  43. [43]

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

    E. Speranza and N. Weickgenannt, “Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics,” Eur. Phys. J. A57no. 5, (2021) 155,arXiv:2007.00138 [nucl-th]

    work page arXiv 2021

  44. [44]

    Dissipative Spin Dynamics in Relativistic Matter,

    S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ryblewski, “Dissipative Spin Dynamics in Relativistic Matter,”Phys. Rev. D103no. 1, (2021) 014030,arXiv:2008.10976 [nucl-th]

    work page arXiv 2021

  45. [45]

    Spin polarization dynamics in the Gubser-expanding background,

    R. Singh, G. Sophys, and R. Ryblewski, “Spin polarization dynamics in the Gubser-expanding background,”Phys. Rev. D103no. 7, (2021) 074024,arXiv:2011.14907 [hep-ph]

    work page arXiv 2021

  46. [46]

    New developments in relativistic fluid dynamics with spin,

    S. Bhadury, J. Bhatt, A. Jaiswal, and A. Kumar, “New developments in relativistic fluid dynamics with spin,”Eur. Phys. J. ST230no. 3, (2021) 655–672,arXiv:2101.11964 [hep-ph]

    work page arXiv 2021

  47. [47]

    Ideal Spin Hydrodynamics from the Wigner Function Approach,

    H.-H. Peng, J.-J. Zhang, X.-L. Sheng, and Q. Wang, “Ideal Spin Hydrodynamics from the Wigner Function Approach,” Chin. Phys. Lett.38no. 11, (2021) 116701,arXiv:2107.00448 [hep-th]

    work page arXiv 2021

  48. [48]

    From Kadanoff-Baym to Boltzmann equations for massive spin-1/2 fermions,

    X.-L. Sheng, N. Weickgenannt, E. Speranza, D. H. Rischke, and Q. Wang, “From Kadanoff-Baym to Boltzmann equations for massive spin-1/2 fermions,”Phys. Rev. D104no. 1, (2021) 016029,arXiv:2103.10636 [nucl-th]

    work page arXiv 2021

  49. [49]

    Lorentz-covariant kinetic theory for massive spin-1/2 particles,

    X.-L. Sheng, Q. Wang, and D. H. Rischke, “Lorentz-covariant kinetic theory for massive spin-1/2 particles,”Phys. Rev. D106no. 11, (2022) L111901,arXiv:2202.10160 [nucl-th]

    work page arXiv 2022

  50. [50]

    Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion,

    J. Hu, “Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion,”Phys. Rev. D105no. 7, (2022) 076009,arXiv:2111.03571 [hep-ph]

    work page arXiv 2022

  51. [51]

    Linear mode analysis from spin transport equation,

    J. Hu, “Linear mode analysis from spin transport equation,”Phys. Rev. D106no. 3, (2022) 036004,arXiv:2202.07373 [hep-ph]

    work page arXiv 2022

  52. [52]

    Quantum kinetic theory for dynamical spin polarization from QED-type interaction,

    S. Fang, S. Pu, and D.-L. Yang, “Quantum kinetic theory for dynamical spin polarization from QED-type interaction,” Phys. Rev. D106no. 1, (2022) 016002,arXiv:2204.11519 [hep-ph]

    work page arXiv 2022

  53. [53]

    Spin evolution of massive fermion in QED plasma,

    Z. Wang, “Spin evolution of massive fermion in QED plasma,”Phys. Rev. D106no. 7, (2022) 076011, arXiv:2205.09334 [hep-ph]

    work page arXiv 2022

  54. [54]

    Relativistic spin hydrodynamics with momentum and spin-dependent relaxation time,

    S. Bhadury, “Relativistic spin hydrodynamics with momentum and spin-dependent relaxation time,”arXiv:2408.14462 [hep-ph]

    work page arXiv

  55. [55]

    The ideal relativistic spinning gas: polarization and spectra

    F. Becattini and F. Piccinini, “The Ideal relativistic spinning gas: Polarization and spectra,”Annals Phys.323(2008) 2452–2473,arXiv:0710.5694 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  56. [56]

    The ideal relativistic rotating gas as a perfect fluid with spin

    F. Becattini and L. Tinti, “The Ideal relativistic rotating gas as a perfect fluid with spin,”Annals Phys.325(2010) 1566–1594,arXiv:0911.0864 [gr-qc]. 53

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  57. [57]

    Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors

    F. Becattini and L. Tinti, “Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors,”Phys. Rev. D87no. 2, (2013) 025029,arXiv:1209.6212 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  58. [58]

    Covariant statistical mechanics and the stress-energy tensor

    F. Becattini, “Covariant statistical mechanics and the stress-energy tensor,”Phys. Rev. Lett.108(2012) 244502, arXiv:1201.5278 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  59. [59]

    Spin tensor and its role in non-equilibrium thermodynamics

    F. Becattini, W. Florkowski, and E. Speranza, “Spin tensor and its role in non-equilibrium thermodynamics,”Phys. Lett.B789(2019) 419–425,arXiv:1807.10994 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  60. [60]

    Kubo formulae for first-order spin hydrodynamics,

    J. Hu, “Kubo formulae for first-order spin hydrodynamics,”Phys. Rev. D103no. 11, (2021) 116015,arXiv:2101.08440 [hep-ph]

    work page arXiv 2021

  61. [61]

    Causality and dissipation in relativistic polarizeable fluids,

    D. Montenegro and G. Torrieri, “Causality and dissipation in relativistic polarizeable fluids,”arXiv:1807.02796 [hep-th]

    work page arXiv

  62. [62]

    Linear response theory and effective action of relativistic hydrodynamics with spin,

    D. Montenegro and G. Torrieri, “Linear response theory and effective action of relativistic hydrodynamics with spin,” Phys. Rev. D102no. 3, (2020) 036007,arXiv:2004.10195 [hep-th]

    work page arXiv 2020

  63. [63]

    Relativistic hydrodynamics for spin-polarized fluids,

    W. Florkowski, A. Kumar, and R. Ryblewski, “Relativistic hydrodynamics for spin-polarized fluids,”Prog. Part. Nucl. Phys.108(2019) 103709,arXiv:1811.04409 [nucl-th]

    work page arXiv 2019

  64. [64]

    Coleman,Lectures of Sidney Coleman on Quantum Field Theory

    S. Coleman,Lectures of Sidney Coleman on Quantum Field Theory. WSP, Hackensack, 12, 2018

    work page 2018

  65. [65]

    On the energy tensor of spinning massive matter in classical field theory and general relativity,

    F. W. Hehl, “On the energy tensor of spinning massive matter in classical field theory and general relativity,”Reports on Mathematical Physics9no. 1, (1976) 55–82

    work page 1976

  66. [66]

    On the spin angular momentum of mesons,

    F. Belinfante, “On the spin angular momentum of mesons,”Physica6no. 7, (1939) 887–898

    work page 1939

  67. [67]

    On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields,

    F. Belinfante, “On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields,”Physica7no. 5, (1940) 449–474

    work page 1940

  68. [68]

    RosenfeldMem

    L. RosenfeldMem. Acad. Roy. Bel.18no. 1, (1940)

    work page 1940

  69. [69]

    S. R. De Groot, W. A. Van Leeuwen, and C. G. Van Weert,Relativistic Kinetic Theory. Principles and Applications. North-Holland Publishing Company, 1980

    work page 1980

  70. [70]

    On the spin angular momentum of the dirac particle,

    J. Hilgevoord and S. Wouthuysen, “On the spin angular momentum of the dirac particle,”Nuclear Physics40(1963) 1 – 12

    work page 1963

  71. [71]

    The covariant definition of spin in relativistic quantum field theory,

    J. Hilgevoord and E. De Kerf, “The covariant definition of spin in relativistic quantum field theory,”Physica31no. 7, (1965) 1002–1016

    work page 1965

  72. [72]

    Pseudogauge dependence of the spin polarization and of the axial vortical effect,

    M. Buzzegoli, “Pseudogauge dependence of the spin polarization and of the axial vortical effect,”Phys. Rev. C105 no. 4, (2022) 044907,arXiv:2109.12084 [nucl-th]

    work page arXiv 2022

  73. [73]

    Pseudogauge dependence of quantum fluctuations of the energy in a hot relativistic gas of fermions,

    A. Das, W. Florkowski, R. Ryblewski, and R. Singh, “Pseudogauge dependence of quantum fluctuations of the energy in a hot relativistic gas of fermions,”Phys. Rev. D103no. 9, (2021) L091502,arXiv:2103.01013 [nucl-th]

    work page arXiv 2021

  74. [74]

    Pseudogauge freedom and the SO(3) algebra of spin operators,

    S. Dey, W. Florkowski, A. Jaiswal, and R. Ryblewski, “Pseudogauge freedom and the SO(3) algebra of spin operators,” Phys. Lett. B843(2023) 137994,arXiv:2303.05271 [hep-th]

    work page arXiv 2023

  75. [75]

    The angular momentum controversy: What's it all about and does it matter?

    E. Leader and C. Lorc´ e, “The angular momentum controversy: What’s it all about and does it matter?,”Phys. Rept. 541no. 3, (2014) 163–248,arXiv:1309.4235 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  76. [76]

    Relativistic distribution function for particles with spin at local thermodynamical equilibrium

    F. Becattini, V. Chandra, L. Del Zanna, and E. Grossi, “Relativistic distribution function for particles with spin at local thermodynamical equilibrium,”Annals Phys.338(2013) 32–49,arXiv:1303.3431 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  77. [77]

    Rindori,Entropy current in relativistic quantum statistical mechanics

    D. Rindori,Entropy current in relativistic quantum statistical mechanics. PhD thesis, U. Florence (main), Florence U., 2020.arXiv:2110.07662 [hep-th]

    work page arXiv 2020

  78. [78]

    Pseudo-gauge invariant non-equilibrium density operator,

    F. Becattini and C. Hoyos, “Pseudo-gauge invariant non-equilibrium density operator,”arXiv:2507.09249 [nucl-th]

    work page arXiv

  79. [79]

    Kubo formulas for relativistic fluids in strong magnetic fields

    X.-G. Huang, A. Sedrakian, and D. H. Rischke, “Kubo formulae for relativistic fluids in strong magnetic fields,”Annals Phys.326(2011) 3075–3094,arXiv:1108.0602 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  80. [80]

    Generalized relativistic second-order spin hydrodynamics from Zubarev’s nonequilibrium statistical operator,

    D. She, Y.-W. Qiu, Z.-F. Jiang, and D. Hou, “Generalized relativistic second-order spin hydrodynamics from Zubarev’s nonequilibrium statistical operator,”Phys. Rev. D112no. 9, (2025) 096013,arXiv:2505.01814 [nucl-th]

    work page arXiv 2025

Showing first 80 references.