pith. machine review for the scientific record. sign in

arxiv: 2603.27353 · v2 · submitted 2026-03-28 · ✦ hep-th · gr-qc

Recognition: 3 theorem links

· Lean Theorem

Universality in Relativistic Spinning Particle Models

Joon-Hwi Kim , Sangmin Lee
Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:33 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords spinning particlesrelativistic modelsmodel equivalenceelectromagnetic couplinggravitational couplingBargmann-Michel-Telegdi equationMathisson-Papapetrou-Dixon equations
0
0 comments X

The pith

Four models of massive spinning particles describe exactly the same physics in four spacetime dimensions.

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

The paper demonstrates that the vector oscillator, spinor oscillator, spherical top, and massive twistor models for relativistic particles carrying spin are physically equivalent. This holds both for free particles and when they interact with electromagnetic or gravitational fields, provided the spin magnitude remains constant. A reader would care because this equivalence unifies disparate approaches in the literature, enabling model-independent derivations of key equations like the Bargmann-Michel-Telegdi and Mathisson-Papapetrou-Dixon equations, and opening the door to consistent inclusion of higher-order spin effects in applications such as black hole physics.

Core claim

Four representative models in the literature—the vector oscillator, spinor oscillator, spherical top, and massive twistor—are shown to describe exactly the same physics in their free and interacting theories with electromagnetism or gravity in four spacetime dimensions within the spin-magnitude-preserving sector. The Bargmann-Michel-Telegdi and quadrupolar Mathisson-Papapetrou-Dixon equations are derived in a model-independent fashion, and the framework allows incorporating higher spin multipole interactions. The interacting theory of the spherical top model is constructed rigorously with emphasis on spin gauge invariance.

What carries the argument

The equivalence mapping between the vector oscillator, spinor oscillator, spherical top, and massive twistor that preserves spin magnitude and produces identical dynamics.

Load-bearing premise

The claimed equivalence is limited to four spacetime dimensions and to the sector where the particle's spin magnitude is preserved.

What would settle it

A calculation showing different trajectories or spin evolutions for the same initial conditions in an electromagnetic field between the vector oscillator and the spherical top models would falsify the equivalence.

read the original abstract

We establish an equivalence between massive spinning particle models in four spacetime dimensions coupled to electromagnetism or gravity, within the spin-magnitude-preserving sector. Four representative models in the literature are shown to describe exactly the same physics in their free and interacting theories: vector oscillator, spinor oscillator, spherical top, and massive twistor. The Bargmann-Michel-Telegdi (BMT) and quadrupolar Mathisson-Papapetrou-Dixon (QMPD) equations are derived in a model-independent fashion. This universal framework allows for incorporating higher spin multipole interactions as well. We establish the rigorous construction of the interacting theory of the spherical top model with emphasis on spin gauge invariance. Applications to black hole physics, conserved charges, and post-Newtonian or post-Minkowskian frameworks are discussed.

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

0 major / 2 minor

Summary. The manuscript claims to establish an exact equivalence among four massive spinning particle models in four spacetime dimensions (vector oscillator, spinor oscillator, spherical top, and massive twistor) within the spin-magnitude-preserving sector. These models are shown to describe identical physics for both free particles and when coupled to electromagnetism or gravity. Model-independent derivations of the Bargmann-Michel-Telegdi (BMT) and quadrupolar Mathisson-Papapetrou-Dixon (QMPD) equations are presented, together with a universal framework for higher spin multipole interactions. A rigorous construction of the interacting spherical top model is given with emphasis on spin gauge invariance, and applications to black hole physics, conserved charges, and post-Newtonian/post-Minkowskian frameworks are discussed.

Significance. If the equivalences hold, the work provides a unifying framework that allows model-independent treatment of spin effects in relativistic particle dynamics. The explicit model-independent derivations of the BMT and QMPD equations, combined with the detailed gauge-invariant construction for the spherical top, strengthen the reliability of results in applications such as black hole physics and precision post-Minkowskian expansions. The extension to higher multipoles offers a systematic route for future generalizations beyond the four models considered.

minor comments (2)
  1. Abstract: the opening sentence could explicitly note the restriction to the spin-magnitude-preserving sector to align immediately with the domain of the claimed equivalences.
  2. Section on model constructions: ensure that the explicit mappings between the four models are accompanied by a brief table summarizing the correspondence of their phase-space variables and constraints.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and constructive report, which accurately captures the scope of our work on the equivalence of the four spinning particle models and the model-independent derivations of the BMT and QMPD equations. The recommendation for minor revision is noted. No specific major comments were listed in the report, so we have no individual points to address point-by-point. Any minor editorial or clarification issues will be incorporated in the revised version.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper establishes equivalence among the four models (vector oscillator, spinor oscillator, spherical top, massive twistor) via explicit constructions in the spin-magnitude-preserving sector of 4D spacetime, and derives the BMT and QMPD equations model-independently. These steps rely on direct mappings and independent derivations rather than reducing to self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations. The central claims remain self-contained with stated domain restrictions and do not collapse to their inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of four-dimensional relativistic physics and the spin-magnitude-preserving restriction; no free parameters, invented entities, or ad-hoc axioms are apparent from the abstract.

axioms (2)
  • domain assumption Four-dimensional spacetime
    All models and equivalences are defined in 4D spacetime as stated.
  • domain assumption Spin magnitude preservation
    Equivalence holds only in the sector where spin magnitude is preserved.

pith-pipeline@v0.9.0 · 5427 in / 1338 out tokens · 63132 ms · 2026-05-14T21:33:29.363579+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.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dynamics of a relativistic discrete body: rigidity conditions, and covariant equations of motion

    gr-qc 2026-05 unverdicted novelty 7.0

    A discrete-particle approach to relativistic rigid bodies is introduced via new rigidity conditions and compatible covariant equations of motion that allow six degrees of freedom.

  2. Dynamics of a relativistic discrete body: rigidity conditions, and covariant equations of motion

    gr-qc 2026-05 unverdicted novelty 7.0

    New Poincaré-covariant rigidity conditions plus equations of motion for a discrete relativistic body give six degrees of freedom and generalize Born's theory.

  3. On the integrability of root-Kerr probe dynamics

    hep-th 2026-04 unverdicted novelty 7.0

    In the root-Kerr model, integrability holds to all spin orders at first order in probe charge with Newman-Janis vertices but extends only to spin-squared at second order and fails at spin-cubic, with asymptotic conser...

  4. On the integrability of root-Kerr probe dynamics

    hep-th 2026-04 unverdicted novelty 6.0

    In the root-Kerr probe model, integrability holds to all spin orders at leading probe charge under Newman-Janis vertices but fails at spin-cubic order at second charge order and cannot be restored by further action de...

Reference graph

Works this paper leans on

213 extracted references · 213 canonical work pages · cited by 2 Pith papers · 47 internal anchors

  1. [1]

    Die Elektrodynamik des rotierenden Elektrons,

    J. Frenkel, “Die Elektrodynamik des rotierenden Elektrons,”Z. Phys.37(1926) 243–262

    work page 1926

  2. [2]

    The Kinematics of an electron with an axis,

    L. H. Thomas, “The Kinematics of an electron with an axis,”Phil. Mag. Ser. 73(1927) 1–21

    work page 1927

  3. [3]

    Neue mechanik materieller systemes,

    M. Mathisson, “Neue mechanik materieller systemes,”Acta Phys. Polon.6(1937) 163–200

    work page 1937

  4. [4]

    Spinning test particles in general relativity. 1.,

    A. Papapetrou, “Spinning test particles in general relativity. 1.,”Proc. Roy. Soc. Lond. A 209(1951) 248–258

    work page 1951

  5. [5]

    Dynamics of extended bodies in general relativity. I. Momentum and angular momentum,

    W. G. Dixon, “Dynamics of extended bodies in general relativity. I. Momentum and angular momentum,”Proc. Roy. Soc. Lond. A314(1970) 499–527. – 98 –

    work page 1970

  6. [6]

    The Relativistic Spherical Top,

    A. J. Hanson and T. Regge, “The Relativistic Spherical Top,”Annals Phys.87(1974) 498

    work page 1974

  7. [7]

    Lagrangian Dynamics of Spinning Particles and Polarized Media in General Relativity,

    I. Bailey and W. Israel, “Lagrangian Dynamics of Spinning Particles and Polarized Media in General Relativity,”Commun. Math. Phys.42(1975) 65–82

    work page 1975

  8. [8]

    Souriau,Structure des syst` emes dynamiques: maˆ ıtrises de math´ ematiques

    J.-M. Souriau,Structure des syst` emes dynamiques: maˆ ıtrises de math´ ematiques. Collection Dunod universit´ e. Dunod, 1970

    work page 1970

  9. [9]

    Sur le mouvement des particules ` a spin en relativit´ e g´ en´ erale,

    J.-M. Souriau, “Sur le mouvement des particules ` a spin en relativit´ e g´ en´ erale,”C. R. Acad. Sc. Paris, S´ erie A271(1970) 751–753

    work page 1970

  10. [10]

    Mod` ele de particule ` a spin dans le champ ´ electromagn´ etique et gravitationnel,

    J.-M. Souriau, “Mod` ele de particule ` a spin dans le champ ´ electromagn´ etique et gravitationnel,”Annales de l’institut Henri Poincar´ e. Section A, Physique Th´ eorique20 no. 4, (1974) 315–364.https://www.numdam.org/item/AIHPA_1974__20_4_315_0/

    work page 1974

  11. [11]

    Canonical dynamics of spinning particles in gravitational and electromagnetic fields,

    H. P. K¨ unzle, “Canonical dynamics of spinning particles in gravitational and electromagnetic fields,”J. Math. Phys.13(1972) 739–744

    work page 1972

  12. [12]

    Classical Charged Particles with Spin,

    P. Grassberger, “Classical Charged Particles with Spin,”J. Phys. A11(1978) 1221

    work page 1978

  13. [13]

    Interaction Vertex for Classical Spinning Particles

    T. Rempel and L. Freidel, “Interaction Vertex for Classical Spinning Particles,”Phys. Rev. D94no. 4, (2016) 044011,arXiv:1507.05826 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  14. [14]

    Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations

    A. A. Deriglazov and W. Guzm´ an Ramirez, “Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations,”Phys. Rev. D92(2015) 124017,arXiv:1509.04926 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  15. [15]

    Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions,

    T. Basile, E. Joung, and T. Oh, “Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions,”JHEP01(2024) 018, arXiv:2307.13644 [hep-th]

    work page arXiv 2024

  16. [16]

    Spinning bodies in general relativity from bosonic worldline oscillators,

    K. Haddad, G. U. Jakobsen, G. Mogull, and J. Plefka, “Spinning bodies in general relativity from bosonic worldline oscillators,”JHEP02(2025) 019,arXiv:2411.08176 [hep-th]

    work page arXiv 2025

  17. [17]

    Particle Spin Dynamics as the Grassmann Variant of Classical Mechanics,

    F. A. Berezin and M. S. Marinov, “Particle Spin Dynamics as the Grassmann Variant of Classical Mechanics,”Annals Phys.104(1977) 336

    work page 1977

  18. [18]

    Relativity and Supersymmetries,

    R. Casalbuoni, “Relativity and Supersymmetries,”Phys. Lett. B62(1976) 49–50

    work page 1976

  19. [19]

    The Classical Mechanics for Bose-Fermi Systems,

    R. Casalbuoni, “The Classical Mechanics for Bose-Fermi Systems,”Nuovo Cim. A33 (1976) 389

    work page 1976

  20. [20]

    Local Supersymmetry for Spinning Particles,

    L. Brink, S. Deser, B. Zumino, P. Di Vecchia, and P. S. Howe, “Local Supersymmetry for Spinning Particles,”Phys. Lett. B64(1976) 435. [Erratum: Phys.Lett.B 68, 488 (1977)]

    work page 1976

  21. [21]

    A Lagrangian Formulation of the Classical and Quantum Dynamics of Spinning Particles,

    L. Brink, P. Di Vecchia, and P. S. Howe, “A Lagrangian Formulation of the Classical and Quantum Dynamics of Spinning Particles,”Nucl. Phys. B118(1977) 76–94

    work page 1977

  22. [22]

    N. M. J. Woodhouse,Geometric quantization. Oxford University Press, 2 ed., 1997

    work page 1997

  23. [23]

    A Universal Model of D=4 Spinning Particle

    S. L. Lyakhovich, A. Y. Segal, and A. A. Sharapov, “A Universal model of D = 4 spinning particle,”Phys. Rev. D54(1996) 5223–5238,arXiv:hep-th/9603174

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  24. [24]

    A Classical and Spinorial Description of the Relativistic Spinning Particle

    T. Rempel and L. Freidel, “A Classical and Spinorial Description of the Relativistic Spinning Particle,”arXiv:1612.00551 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  25. [25]

    Spinor (super)particle with a commuting index spinor,

    V. G. Zima and S. Fedoruk, “Spinor (super)particle with a commuting index spinor,”JETP Lett.61(1995) 251–256

    work page 1995

  26. [26]

    Twistors and the massive spinning particle

    L. Mezincescu, A. J. Routh, and P. K. Townsend, “Twistors and the massive spinning particle,”J. Phys. A49no. 2, (2016) 025401,arXiv:1508.05350 [hep-th]. – 99 –

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  27. [27]

    Twistors and particles: An outline,

    R. Penrose, “Twistors and particles: An outline,” inFeldafing Conference of the Max-Planck Inst. on Quantum Theory and the Structure of Space-time, pp. 129–145. 1974

    work page 1974

  28. [28]

    Twistor variables of relativistic mechanics,

    Z. Perj´ es, “Twistor variables of relativistic mechanics,”Phys. Rev. D11(1975) 2031–2041

    work page 1975

  29. [29]

    Some symplectic forms arising in twistor theory,

    P. Tod, “Some symplectic forms arising in twistor theory,”Reports on Mathematical Physics11no. 3, (1977) 339–346

    work page 1977

  30. [30]

    On Lorentz particle with spin. A twistorial approach,

    A. Bette, “On Lorentz particle with spin. A twistorial approach,”Rept. Math. Phys.28 (1989) 133–140

    work page 1989

  31. [31]

    Massive Relativistic Particle Model with Spin and Electric Charge from Two-Twistor Dynamics

    A. Bette, J. A. de Azcarraga, J. Lukierski, and C. Miquel-Espanya, “Massive relativistic particle model with spin and electric charge from two-twistor dynamics,”Phys. Lett. B595 (2004) 491–497,arXiv:hep-th/0405166

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  32. [32]

    Bitwistor formulation of massive spinning particle

    S. Fedoruk and V. G. Zima, “Bitwistor formulation of massive spinning particle,” arXiv:hep-th/0308154

    work page internal anchor Pith review Pith/arXiv arXiv

  33. [33]

    Massive Particle Model with Spin from a Hybrid (spacetime-twistorial) Phase Space Geometry and Its Quantization

    S. Fedoruk, A. Frydryszak, J. Lukierski, and C. Miquel-Espanya, “Massive particle model with spin from a hybrid (spacetime-twistorial) phase space geometry and its quantization,” in22nd Max Born Symposium on Quantum, Super and Twistors: A Conference in Honor of Jerzy Lukierski on His 70th Birthday. 2, 2007.arXiv:hep-th/0702050

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  34. [34]

    Massive twistor particle with spin generated by Souriau-Wess-Zumino term and its quantization

    S. Fedoruk and J. Lukierski, “Massive twistor particle with spin generated by Souriau–Wess–Zumino term and its quantization,”Phys. Lett. B733(2014) 309–315, arXiv:1403.4127 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  35. [35]

    Two-twistor particle models and free massive higher spin fields

    J. A. de Azcarraga, S. Fedoruk, J. M. Izquierdo, and J. Lukierski, “Two-twistor particle models and free massive higher spin fields,”JHEP04(2015) 010,arXiv:1409.7169 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  36. [36]

    Gauged twistor formulation of a massive spinning particle in four dimensions

    S. Deguchi and S. Okano, “Gauged twistor formulation of a massive spinning particle in four dimensions,”Phys. Rev. D93no. 4, (2016) 045016,arXiv:1512.07740 [hep-th]. [Erratum: Phys.Rev.D 93, 089906 (2016)]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  37. [37]

    The relativistic spherical top as a massive twistor,

    J.-H. Kim, J.-W. Kim, and S. Lee, “The relativistic spherical top as a massive twistor,”J. Phys. A54no. 33, (2021) 335203,arXiv:2102.07063 [hep-th]

    work page arXiv 2021

  38. [38]

    Symplectic Perturbation Theory in Massive Ambitwistor Space: A Zig-Zag Theory of Massive Spinning Particles,

    J.-H. Kim and S. Lee, “Symplectic Perturbation Theory in Massive Ambitwistor Space: A Zig-Zag Theory of Massive Spinning Particles,”arXiv:2301.06203 [hep-th]

    work page arXiv

  39. [39]

    Lagrangian Models of the Particles with Spin: The First Seventy Years

    A. Frydryszak, “Lagrangian models of the particles with spin: The First seventy years,” arXiv:hep-th/9601020

    work page internal anchor Pith review Pith/arXiv arXiv

  40. [40]

    Rivas,Kinematical Theory of Spinning Particles

    M. Rivas,Kinematical Theory of Spinning Particles. Springer Dordrecht, 2002

    work page 2002

  41. [41]

    Lagrangian formulation for the massless (super)particles in (super)twistor approach,

    M. S. Plyushchay, “Lagrangian formulation for the massless (super)particles in (super)twistor approach,”Phys. Lett. B240(1990) 133–136

    work page 1990

  42. [42]

    Pseudoclassical description of the massive spinning particle in d-dimensions,

    M. S. Plyushchay, “Pseudoclassical description of the massive spinning particle in d-dimensions,”Mod. Phys. Lett. A8(1993) 937–945

    work page 1993

  43. [43]

    Single twistor description of massless, massive, AdS, and other interacting particles

    I. Bars and M. Picon, “Single twistor description of massless, massive, AdS, and other interacting particles,”Phys. Rev. D73(2006) 064002,arXiv:hep-th/0512091

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  44. [44]

    Twistor Transform in d Dimensions and a Unifying Role for Twistors

    I. Bars and M. Picon, “Twistor transform in d dimensions and a unifying role for twistors,” Phys. Rev. D73(2006) 064033,arXiv:hep-th/0512348

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  45. [45]

    Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity

    A. A. Deriglazov and W. Guzm´ an Ramirez, “Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic – 100 – moment in General Relativity,”Adv. Math. Phys.2017(2017) 7397159, arXiv:1710.07135 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  46. [46]

    Spin and Susceptibility Effects of Electromagnetic Self-Force in Effective Field Theory,

    G. U. Jakobsen, “Spin and Susceptibility Effects of Electromagnetic Self-Force in Effective Field Theory,”Phys. Rev. Lett.132no. 15, (2024) 151601,arXiv:2311.04151 [hep-th]

    work page arXiv 2024

  47. [47]

    Editorial note to: On the motion of spinning particles in general relativity by Jean-Marie Souriau,

    T. Damour and P. Iglesias-Zemmour, “Editorial note to: On the motion of spinning particles in general relativity by Jean-Marie Souriau,”Gen. Rel. Grav.56no. 10, (2024) 127,arXiv:2401.10013 [gr-qc]

    work page arXiv 2024

  48. [48]

    Asymptotic spinspacetime,

    J.-H. Kim, “Asymptotic spinspacetime,”Phys. Rev. D111no. 10, (2025) 105011, arXiv:2309.11886 [hep-th]

    work page arXiv 2025

  49. [49]

    Massive twistor worldline in electromagnetic fields,

    J.-H. Kim, J.-W. Kim, and S. Lee, “Massive twistor worldline in electromagnetic fields,” JHEP08(2024) 080,arXiv:2405.17056 [hep-th]

    work page arXiv 2024

  50. [50]

    Precession of the polarization of particles moving in a homogeneous electromagnetic field,

    V. Bargmann, L. Michel, and V. L. Telegdi, “Precession of the polarization of particles moving in a homogeneous electromagnetic field,”Phys. Rev. Lett.2(1959) 435–436

    work page 1959

  51. [51]

    A. A. Kirillov,Elements of the Theory of Representations. Berlin, Heidelberg, New York: Springer 1975, Chap. 15, 1975

    work page 1975

  52. [52]

    Orbits and quantization theory,

    B. Kostant, “Orbits and quantization theory,” inProc. Int. Cong. Math., Nice, vol. 2, p. 395. 1970

    work page 1970

  53. [53]

    Space-time and degrees of freedom of the elementary particle,

    H. Bacry, “Space-time and degrees of freedom of the elementary particle,”Communications in Mathematical Physics5no. 2, (1967) 97–105

    work page 1967

  54. [54]

    Classical Lorentz invariant particles,

    R. Arens, “Classical Lorentz invariant particles,”Journal of Mathematical Physics12 no. 12, (1971) 2415–2422

    work page 1971

  55. [55]

    Relativistic Quantum Kinematics in the Moyal Representation,

    J. F. Carinena, J. M. Gracia-Bondia, and J. C. Varilly, “Relativistic Quantum Kinematics in the Moyal Representation,”J. Phys. A23(1990) 901

    work page 1990

  56. [56]

    The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles,

    M. H. L. Pryce, “The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles,”Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences195no. 1040, (1948) 62–81

    work page 1948

  57. [57]

    Localized states for elementary systems,

    T. D. Newton and E. P. Wigner, “Localized states for elementary systems,”Rev. Mod. Phys.21(1949) 400–406

    work page 1949

  58. [58]

    Sur la dynamique des syst` emes ayant un moment angulaire interne,

    C. Møller, “Sur la dynamique des syst` emes ayant un moment angulaire interne,”Annales de l’institut Henri Poincar´ e11no. 5, (1949) 251–278

    work page 1949

  59. [59]

    On the definition of the centre of gravity of an arbitrary closed system in the theory of relativity,

    C. Møller, “On the definition of the centre of gravity of an arbitrary closed system in the theory of relativity,”Communications of the Dublin Institute for Advanced Studiesno. 5, (1949) 3–42

    work page 1949

  60. [60]

    Covariant position operators, spin, and locality,

    G. N. Fleming, “Covariant position operators, spin, and locality,”Physical Review137 no. 1B, (1965) B188

    work page 1965

  61. [61]

    Dynamics of extended bodies in general relativity. II. Moments of the charge-current vector,

    W. G. Dixon, “Dynamics of extended bodies in general relativity. II. Moments of the charge-current vector,”Proc. Roy. Soc. Lond. A319(1970) 509–547

    work page 1970

  62. [62]

    Center of mass, spin supplementary conditions, and the momentum of spinning particles

    L. F. O. Costa and J. Nat´ ario, “Center of mass, spin supplementary conditions, and the momentum of spinning particles,”Fund. Theor. Phys.179(2015) 215–258, arXiv:1410.6443 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  63. [63]

    Spin supplementary conditions for spinning compact binaries

    B. Mik´ oczi, “Spin supplementary conditions for spinning compact binaries,”Phys. Rev. D 95no. 6, (2017) 064023,arXiv:1609.01536 [gr-qc]. – 101 –

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  64. [64]

    Hamiltonians and canonical coordinates for spinning particles in curved space-time

    V. Witzany, J. Steinhoff, and G. Lukes-Gerakopoulos, “Hamiltonians and canonical coordinates for spinning particles in curved space-time,”Class. Quant. Grav.36no. 7, (2019) 075003,arXiv:1808.06582 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  65. [65]

    Spin gauge symmetry in the action principle for classical relativistic particles

    J. Steinhoff, “Spin gauge symmetry in the action principle for classical relativistic particles,”arXiv:1501.04951 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv

  66. [66]

    Multipolar equations of motion for extended test bodies in General Relativity

    J. Steinhoff and D. Puetzfeld, “Multipolar equations of motion for extended test bodies in General Relativity,”Phys. Rev. D81(2010) 044019,arXiv:0909.3756 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  67. [67]

    Mechanics of extended masses in general relativity

    A. I. Harte, “Mechanics of extended masses in general relativity,”Class. Quant. Grav.29 (2012) 055012,arXiv:1103.0543 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  68. [68]

    Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin,

    J. Vines, D. Kunst, J. Steinhoff, and T. Hinderer, “Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin,”Phys. Rev. D93no. 10, (2016) 103008,arXiv:1601.07529 [gr-qc]. [Erratum: Phys.Rev.D 104, 029902 (2021)]

    work page arXiv 2016

  69. [69]

    Generalized Carter constant for quadrupolar test bodies in Kerr spacetime,

    G. Comp` ere, A. Druart, and J. Vines, “Generalized Carter constant for quadrupolar test bodies in Kerr spacetime,”SciPost Phys.15no. 6, (2023) 226,arXiv:2302.14549 [gr-qc]

    work page arXiv 2023

  70. [70]

    Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown,

    P. Ramond, S. Isoyama, and A. Druart, “Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown,”arXiv:2601.06416 [gr-qc]

    work page arXiv

  71. [71]

    Particle with internal angular momentum in a gravitational field,

    I. Khriplovich, “Particle with internal angular momentum in a gravitational field,”Soviet Physics-JETP (English Translation)69no. 2, (1989) 217–219

    work page 1989

  72. [72]

    Equations of Motion for Spinning Particles in External\\Electromagnetic and Gravitational Fields

    K. Yee and M. Bander, “Equations of motion for spinning particles in external electromagnetic and gravitational fields,”Phys. Rev. D48(1993) 2797–2799, arXiv:hep-th/9302117

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  73. [73]

    Equations of Motion of Spinning Relativistic Particle in External Fields

    I. B. Khriplovich and A. A. Pomeransky, “Equations of motion of spinning relativistic particle in external fields,”J. Exp. Theor. Phys.86(1998) 839–849,arXiv:gr-qc/9710098

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  74. [74]

    Laws of motion and precession for black holes and other bodies,

    K. S. Thorne and J. B. Hartle, “Laws of motion and precession for black holes and other bodies,”Phys. Rev. D31(1984) 1815–1837

    work page 1984

  75. [75]

    Feynman’s proof of the maxwell equations,

    F. J. Dyson, “Feynman’s proof of the maxwell equations,”American Journal of Physics58 no. 3, (1990) 209–211

    work page 1990

  76. [76]

    The Feynman-Dyson proof of the gauge field equations,

    C. Lee, “The Feynman-Dyson proof of the gauge field equations,”Physics letters A148 no. 3-4, (1990) 146–148

    work page 1990

  77. [77]

    Relativistic generalization and extension to the non-Abelian gauge theory of Feynman’s proof of the Maxwell equations,

    S. Tanimura, “Relativistic generalization and extension to the non-Abelian gauge theory of Feynman’s proof of the Maxwell equations,”Annals of Physics220no. 2, (1992) 229–247

    work page 1992

  78. [78]

    Deformed Wong particles,

    A. Stern and I. Yakushin, “Deformed Wong particles,”Physical Review D48no. 10, (1993) 4974

    work page 1993

  79. [79]

    Dynamical equations of spinning particles. Feynman’s proof,

    C. Chou, “Dynamical equations of spinning particles. Feynman’s proof,”Physics Letters B 323no. 2, (1994) 147–152

    work page 1994

  80. [80]

    Dirac monopole with Feynman brackets,

    A. B´ erard, Y. Grandati, and H. Mohrbach, “Dirac monopole with Feynman brackets,” Physics Letters A254no. 3-4, (1999) 133–136

    work page 1999

Showing first 80 references.