Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Peierls substitution and Hall motion in exotic Carroll dynamics

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Charged exotic Carroll particles obey an anomalous Hall law, and the DJT Peierls model is their common reduction with critical Galilean dynamics.

desk verdict Regular-case exotic Carroll Hall motion is solid; the critical-point reduction to DJT is a formal limit rather than a true equivalence, and that weakens the paper's headline claim. read the letter →

arxiv 2411.14329 v4 pith:6VWKURYG submitted 2024-11-21 hep-th math-phmath.MP

H.-X. Zeng , Q.-L. Zhao , P.-M. Zhang , P. A. Horvathy This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords CarrollsymmetryexoticparticlePeierlssubstitutionDunne-Jackiw-TrugenbergersystemanomalousHalleffectcentralextensionnoncommutativecoordinatesblackholehorizon
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Carrollian particles are famously immobile, because Carroll boosts shift time rather than position. This paper argues that the recently discovered two-parameter central extension of the planar Carroll group breaks that immobility: a charged exotic Carroll particle in constant planar fields moves by an anomalous Hall law, drifting perpendicular to the electric field with a speed fixed by the noncommutativity parameter $\theta$ and the effective magnetic field $B^*$. The same first-order Dunne-Jackiw-Trugenberger model used to justify the Peierls substitution is shown to arise by reduction from both exotic Galilean and exotic Carroll systems, with the guiding centre identified with the DJT position. If the paper is right, the Peierls-substitution model is a common reduction of two dual symmetry frameworks, and Carroll dynamics acquires a concrete transport phenomenon.

What carries the argument

The load-bearing object is the two-parameter central extension of the planar Carroll group, with parameters $\kappa_{\mathrm{exo}}$ and $\kappa_{\mathrm{mag}}$ entering through $\theta = \kappa_{\mathrm{exo}}/m^2$ and $B^* = eB + \kappa_{\mathrm{mag}}$ in the Souriau form (IV.2), a closed two-form whose kernel gives the equations of motion and which encodes both noncommuting coordinates and an internal magnetic field. From that form the paper derives first-order equations of motion that are decoupled between $x$ and $p$, and a guiding-centre coordinate $Q_i = x_i + \frac{1}{B^*}\epsilon_{ij}p_j$ that survives the singular critical limit $m^* = 0$. Hamiltonian reduction in the critical case leaves $Q$ as the only dynamical variable, with a symplectic form and Hamiltonian matching the DJT system, which is the mechanism behind Proposition IV.7. The chiral decomposition $x_i = X^+_i + X^-_i$ with $X^+ = Q$ splits the motion into a standard Hall part and an anomalous part, making the partial immobility and the half-Carroll symmetry explicit.

What would settle it

A first-principles cohomology calculation of the planar Carroll group that produces a two-parameter cocycle different from Eq. (IV.2), or an independent Hamiltonian reduction of the Carroll Lagrangian (IV.4) that does not yield the DJT system (II.1), would refute the paper's central claim.

Watch

Extended reading notes

Core claim

The paper's central claim is Proposition IV.1: for an exotic Carroll particle with nonvanishing effective mass $m^* = 1 - \theta B^*$, the position obeys $\dot{x}_i = -\frac{e\theta}{1-\theta B^*}\,\epsilon_{ij}E_j$, so the particle performs anomalous Hall motion in Carroll time, while the momentum obeys an independent equation and does not feed back into the position. Proposition IV.7 then states that at the critical point where the effective mass vanishes, the reduced Carroll system projects onto the same DJT Hall motion as the critical Galilean system, with the guiding centre $Q$ identified with the DJT position $\xi$. The dynamics inherits a "half-Carroll" boost symmetry: boosts along the electric field remain symmetries, while boosts perpendicular to it are broken, and the conserved quantity $K_\parallel$ is tied to the absence of motion along the field. Switching off the exotic parameter $\theta$ restores the immobility of unextended Carroll particles, so the motion is entirely due to the central extension. The same structure maps by duality to an uncharged anyon on a black-hole horizon, where the spin-Hall effect replaces the anomalous Hall effect.

Load-bearing premise

The argument takes as given the earlier claim that the planar Carroll group has a two-parameter central extension with exactly the cocycle used here, plus the potential-only form of the Carroll Hamiltonian; if those imported inputs are wrong, the anomalous Hall law and the DJT reduction do not follow.

Editorial extensions

If this is right

  • A charged exotic Carroll particle in constant electromagnetic fields drifts with a velocity set by the anomalous Hall coefficient, so Carroll particles are not intrinsically immobile when the two-parameter extension is present.
  • The DJT or Peierls-substitution model is a common reduction of both exotic Galilean and exotic Carroll dynamics; identifying the guiding centre with the DJT position makes the two projections coincide.
  • Switching off the exotic parameter $\theta$ recovers the celebrated immobility of unextended Carroll particles, showing that the motion is generated by the central extension rather than by the external fields alone.
  • At $\theta\kappa_{\mathrm{mag}} = 1$ the anomalous Hall law reduces to the ordinary Hall law, and when $B=0$ Hall-like motion persists, so the second Carroll charge $\kappa_{\mathrm{mag}}$ behaves as an internal magnetic field.
  • One Carroll boost generator survives the electromagnetic field while the other is broken, yielding a half-Carroll symmetry whose conserved quantity forbids motion along the electric field.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the Carroll reduction is robust, the Peierls-substitution kinematics may describe low-energy quasiparticles whose emergent symmetry is Carrollian rather than only Galilean, and the anomalous Hall coefficient could be probed in tilted-field or synthetic-gauge-field experiments.
  • The duality with black-hole-horizon anyons suggests the same anomalous Hall dynamics governs horizon-localised excitations, so horizon spin-Hall drift could serve as a gravitational test of the Carroll model.
  • The half-Carroll symmetry pattern may be a general signature of first-order or singular dynamical systems, where partially broken boosts accompany constrained, potential-dominated motion.
  • A natural extension beyond this paper is to position-dependent fields: the anomalous Hall law would then acquire gradient corrections, potentially linking the model to the vortex dynamics the paper announces as forthcoming.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper studies the 'exotic' Carroll particle associated with the two-parameter central extension of the planar Carroll group. In a constant electromagnetic field, the regular case (m* ≠ 0) yields an anomalous Hall law for the position (Eq. IV.7) and a linear growth for the momentum (Eq. IV.8). The paper then claims that, in the singular case m* = 0, a Hamiltonian reduction of the exotic Carroll system produces the Dunne-Jackiw-Trugenberger (DJT) system, whose position follows the ordinary Hall law (Eq. II.2). The authors also analyze boost symmetries, finding a half-Carroll symmetry, and discuss a duality with anyonic motion on a black hole horizon. The comparison with the exotic Galilean derivation of DJT is emphasized throughout.

Significance. If the central claims hold, the paper establishes a new Carrollian route to the DJT/Peierls-substitution system, complementing the known Galilean derivation, and shows that exotic Carroll particles are mobile while recovering immobility when the exotic extension is switched off. The symplectic computations are explicit and the propositions are mostly accompanied by derivations. However, the load-bearing critical-case reduction (Prop. IV.4 and IV.7) requires a clearer justification, because the original Carroll equations are inconsistent at exactly m* = 0 for E ≠ 0.

major comments (2)
  1. [Sec. IV.A, Eqs. (IV.5) and (IV.15)-(IV.23)] The claim that the critical Carroll system (m* = 0) reduces to the DJT Hall motion is not supported by a reduction of the original solution space. As the authors themselves note, at m* = 0 Eqs. (IV.5) read 0 = -eθ ε_ij E_j and 0 = eE_i, which admit no solution for E ≠ 0. The limiting procedure based on the canonical transformation (IV.15) defines a new effective model (IV.22)-(IV.23), but it does not project the dynamics of (IV.5), whose solution space is empty. To make Prop. IV.7 valid, the authors must either provide a genuine Faddeev-Jackiw reduction of the singular Carroll system (which would have to confront the inconsistency) or explicitly state that DJT emerges only as a singular limit or regularization of the regular Carroll dynamics.
  2. [Sec. IV.A, Eqs. (IV.18) and (IV.22)-(IV.23)] The derivation of the reduced Hall law (IV.23) from the canonical equations (IV.18) is not transparent: taking m* → 0 in (IV.18) gives a divergent velocity for Q, not the finite Hall law. The finite result is obtained only after imposing the constraint (IV.20) and using the reduced symplectic form (IV.22). The paper should clarify the order of limits and justify why the divergent term is discarded, or alternatively formulate the reduction directly on the singular Souriau form.
minor comments (5)
  1. [Abstract] The phrase 'position and momentum follow uncoupled anomalous Hall motions' is inaccurate for the momentum, since Eq. (IV.8) describes linear acceleration along E, not a Hall-type perpendicular drift; consider rewording.
  2. [Eq. (IV.29)] The notation 'eQi' is undefined and appears to be a typesetting artifact; please define the guiding centre used at that point.
  3. [Eq. (IV.23) and Prop. IV.4] The stated Hall law omits the electric charge e. From the reduced Hamiltonian Hred = -eE_i Q_i and the bracket {Q1,Q2} = -1/B*, the equations of motion give ˙Q_i = (e/B*_crit) ε_ij E_j, not (1/B*_crit) ε_ij E_j, unless B* = eB; please correct the formula or explain the convention.
  4. [Sec. VI] Eq. (VI.1) is imported from Ref. [23] without derivation; a brief reminder of the setup would make the black-hole-horizon discussion self-contained.
  5. [Sec. II] There is a typo in the sentence 'In the next section we show tht the DJT system...' — 'tht' should be 'that'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the Carroll-to-DJT reduction is a genuine computation from an imported Souriau form, not a restatement of its inputs.

full rationale

The central chain is: the exotic Carroll Souriau form (IV.2), with B* = eB + kappa_mag and theta = kappa_exo/m^2, is imported from Refs. [4-7]; from it the paper derives the first-order equations (IV.5); solving those equations for the velocity yields the anomalous Hall law (IV.7). That step is algebraic and is not built into the definition of the Souriau form. The Carroll-to-DJT reduction in Sec. IV.A is also a computation: canonical coordinates (IV.15) are introduced, the reduced symplectic form, Poisson brackets and Hamiltonian are derived in (IV.22), and the resulting Hall motion (IV.23) is identified with the DJT Souriau form (II.5). The identification is made after the reduction, not assumed before it. The paper's self-citations, including Ref. [28] and Marsot's Ref. [7], supply the input model, but that model is mathematically specified and does not already contain the reduction result; the derivation chain is therefore not circular. The singular m* = 0 case is delicate: as the paper itself states in Sec. IV.A, both equations in (IV.5) are contradictory unless eE = 0, so Prop. IV.7 is best read as a Hamiltonian-reduction/limiting statement rather than a literal equivalence of the original critical dynamics. That is a domain or correctness concern, not a circularity, and it does not affect the regular-case anomalous Hall law (IV.7).

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the pre-existing two-parameter Carroll central extension and the naked-potential Hamiltonian, both cited from prior work, plus standard symplectic reduction. No data are fitted; θ and κ_mag are arbitrary extension parameters, not numbers tuned to match experiments. No new particles, forces, or dimensions are introduced.

free parameters (2)
  • θ (noncommutativity parameter, κ_exo/m²)
    Central-extension parameter from the planar Carroll group, chosen by hand; it controls the anomalous Hall velocity in Eq. (IV.7) and is varied in Fig. 2.
  • κ_mag (second Carroll extension parameter)
    Acts as an internal magnetic field added to eB in B* = eB + κ_mag (IV.1); not fitted to data, but the central Hall result depends on it.
assumptions (4)
  • domain assumption Existence and exact form of the two-parameter central extension of the planar Carroll group, yielding the Souriau form (IV.2).
    Taken from Refs. [3-7]; load-bearing because Eq. (IV.2) generates all dynamics. Cited, not re-derived.
  • domain assumption The Carroll particle Hamiltonian is the naked potential H = eV with no kinetic term (IV.3).
    This is the defining feature of the exotic Carroll model from [7]; the anomalous Hall law depends critically on the absence of a p²/(2m) term.
  • standard math Faddeev-Jackiw Hamiltonian reduction is valid for the singular case m* = 0.
    Used in Sec. IV.A to derive the reduced guiding-centre dynamics (IV.22)-(IV.23).
  • domain assumption Constant electromagnetic fields E and B in the plane.
    Assumed in Sec. II and throughout; closed-form solutions and Hall laws are derived for this case only.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Peierls substitution and Hall motion in exotic Carroll dynamics." pith.science (2026). https://pith.science/paper/6VWKURYG

@misc{pith2026241114329,
  author       = {Pith},
  title        = {Pith review of: Peierls substitution and Hall motion in exotic Carroll dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6VWKURYG}},
  note         = {Machine review of arXiv:2411.14329}
}
abstract

The particle with first-order dynamics proposed by Dunne, Jackiw and Trugenberger (DJT) to justify the ``Peierls substitution" is obtained by reduction from both of the planar two-parameter centrally extended Galilean and Carroll systems. In the latter case the extension parameters $\kappa_{exo}$ and $\kappa_{mag}$ generate non-commutativity of the coordinates resp. behave as an internal magnetic field. The position and momentum follow uncoupled anomalous Hall motions. Consistently with partial immobility, one of the Carroll boost generators is broken but the other remains a symmetry. Switching off $\kappa_{exo}$, the immobility of unextended Carroll particles is recovered. The Carroll system is dual to an uncharged anyon on the horizon of a black hole which exhibits the spin-Hall effect. Physical applications are shortly reviewed.

Figures

Figures reproduced from arXiv: 2411.14329 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. BMS$_3$ invariant field theories

    hep-th 2026-07 accept novelty 6.0 of 10

    New BMS3-invariant 2D scalar theories (electric, magnetic, canonical, coupled) with boundary analysis, flux laws, monodromy matching to 3D gravity, and complementary AdS3/dS3 flat limits.

Reference graph

Works this paper leans on

75 extracted references · 36 canonical work pages · cited by 1 Pith paper

  1. [1]

    Une nouvelle limite non-relativiste du group de Poincar´ e,

    J. M. L´ evy-Leblond, “Une nouvelle limite non-relativiste du group de Poincar´ e,” Ann. Inst. H Poincar´ e3 (1965) 1

    work page 1965

  2. [2]

    On an Analogue of the Galileo Group,

    V. D. Sen Gupta, “On an Analogue of the Galileo Group,” Il Nuovo Cimento 54 (1966) 512

    work page 1966

  3. [3]

    Central exten- sions of the quasiorthogonal Lie algebras,

    J. A. de Azcarraga, F. J. Herranz, J. C. Perez Bueno and M. Santander, “Central exten- sions of the quasiorthogonal Lie algebras,” J. Phys. A 31 (1998), 1373-1394 doi:10.1088/0305- 4470/31/5/008 [arXiv:q-alg/9612021 [math.QA]]

    arXiv 1998

  4. [4]

    Noncommutative Phase Spaces by Coadjoint Orbits Method

    A. Ngendakumana and J. Nzotungicimpaye, “Noncommutative Phase Spaces by Coadjoint Orbits Method,” SIGMA 7 (2011), 116 doi:10.3842/SIGMA.2011.116 [arXiv:1102.0718 [math- ph]]. 22

    work page Pith review arXiv 2011

  5. [5]

    Group theoretical con- struction of planar Noncommutative Phase Spaces,

    A. Ngendakumana, J. Nzotungicimpaye and L. Todjihounde, “Group theoretical con- struction of planar Noncommutative Phase Spaces,” J. Math. Phys. 55 (2014), 013508 doi:10.1063/1.4862843 [arXiv:1308.3065 [math-ph]]

    arXiv 2014

  6. [6]

    Group Theoretical Construction of Planar Noncommutative Systems

    A. Ngendakumana, “Group Theoretical Construction of Planar Noncommutative Systems,” [arXiv:1401.5213 [math-ph]]

    work page Pith review arXiv

  7. [7]

    Planar Carrollean dynamics, and the Carroll quantum equation,

    L. Marsot, “Planar Carrollean dynamics, and the Carroll quantum equation,” J. Geom. Phys. 179 (2022), 104574 doi:10.1016/j.geomphys.2022.104574 [arXiv:2110.08489 [math-ph]]

    work page arXiv 2022

  8. [8]

    Galilei group and Galilean invariance,

    J.-M. L´ evy-Leblond, “Galilei group and Galilean invariance,” in Group Theory and Applica- tions, Loebl Ed., II, Acad. Press, New York, p. 222 (1972)

    work page 1972

Show all 75 references
  1. [9]

    Bargmann Structures and Newton-cartan Theory,

    C. Duval, G. Burdet, H. P. Kunzle and M. Perrin, “Bargmann Structures and Newton-cartan Theory,” Phys. Rev. D 31 (1985), 1841-1853 doi:10.1103/PhysRevD.31.1841

    1985 doi

  2. [10]

    Celestial mechanics, conformal structures and gravitational waves,

    C. Duval, G. W. Gibbons and P. Horvathy, “Celestial mechanics, conformal structures and gravitational waves,” Phys. Rev. D 43 (1991), 3907-3922 doi:10.1103/PhysRevD.43.3907 [arXiv:hep-th/0512188 [hep-th]]

    1991 arXiv

  3. [11]

    Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time,

    C. Duval, G. W. Gibbons, P. A. Horvathy and P. M. Zhang, “Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time,” Class. Quant. Grav. 31 (2014) 085016 [arXiv:1402.0657 [gr-qc]]

    2014 arXiv

  4. [12]

    On Unitary ray representations of continuous groups,

    V. Bargmann, “On Unitary ray representations of continuous groups,” Annals Math. 59 (1954), 1-46 doi:10.2307/1969831

    1954 doi

  5. [13]

    Carroll Symmetry, Dark Energy and Inflation,

    J. de Boer, J. Hartong, N. A. Obers, W. Sybesma and S. Vandoren, “Carroll Symmetry, Dark Energy and Inflation,” Front. in Phys. 10 (2022), 810405 doi:10.3389/fphy.2022.810405 [arXiv:2110.02319 [hep-th]]

    2022

  6. [14]

    Dynamics of Carroll Particles,

    E. Bergshoeff, J. Gomis and G. Longhi, “Dynamics of Carroll Particles,” Class. Quant. Grav. 31 (2014) no.20, 205009 doi:10.1088/0264-9381/31/20/205009 [arXiv:1405.2264 [hep-th]]

    2014 arXiv

  7. [15]

    Embedding nonrelativistic physics inside a gravitational wave,

    X. Bekaert and K. Morand, “Embedding nonrelativistic physics inside a gravitational wave,” Phys. Rev. D 88 (2013) no.6, 063008 doi:10.1103/PhysRevD.88.063008 [arXiv:1307.6263 [hep- th]]

    2013 arXiv

  8. [16]

    Embedding Galilean and Carrollian geometries I. Gravitational waves,

    K. Morand, “Embedding Galilean and Carrollian geometries I. Gravitational waves,” J. Math. Phys. 61 (2020) no.8, 082502 doi:10.1063/1.5130907 [arXiv:1811.12681 [hep-th]]

    2020 arXiv

  9. [17]

    Carroll stories,

    J. de Boer, J. Hartong, N. A. Obers, W. Sybesma and S. Vandoren, “Carroll stories,” JHEP 09 (2023), 148 doi:10.1007/JHEP09(2023)148 [arXiv:2307.06827 [hep-th]]. 23

    2023 arXiv

  10. [18]

    Tachyon condensates, Carrollian contraction of Lorentz group, and fundamental strings,

    G. Gibbons, K. Hashimoto and P. Yi, “Tachyon condensates, Carrollian contraction of Lorentz group, and fundamental strings,” JHEP 09 (2002), 061 doi:10.1088/1126-6708/2002/09/061 [arXiv:hep-th/0209034 [hep-th]]

    2002 arXiv

  11. [19]

    Carroll symmetry of plane grav- itational waves,

    C. Duval, G. W. Gibbons, P. A. Horvathy and P. M. Zhang, “Carroll symmetry of plane grav- itational waves,” Class. Quant. Grav. 34 (2017) no.17, 175003 doi:10.1088/1361-6382/aa7f62 [arXiv:1702.08284 [gr-qc]]

    2017 arXiv

  12. [20]

    Carrollian Physics at the Black Hole Horizon,

    L. Donnay and C. Marteau, “Carrollian Physics at the Black Hole Horizon,” Class. Quant. Grav. 36 (2019) no.16, 165002 doi:10.1088/1361-6382/ab2fd5 [arXiv:1903.09654 [hep-th]]

    2019 arXiv

  13. [21]

    Carrollian Perspective on Celestial Holography,

    L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi, “Carrollian Perspective on Celestial Holography,” Phys. Rev. Lett. 129 (2022) no.7, 071602 doi:10.1103/PhysRevLett.129.071602 [arXiv:2202.04702 [hep-th]]

    2022 arXiv

  14. [22]

    Bridging Carrollian and celestial holography,

    L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi, “Bridging Carrollian and celestial holography,” Phys. Rev. D 107 (2023) no.12, 126027 doi:10.1103/PhysRevD.107.126027 [arXiv:2212.12553 [hep-th]]

    2023 arXiv

  15. [23]

    Anyonic spin-Hall effect on the black hole horizon,

    L. Marsot, P. M. Zhang and P. Horvathy, “Anyonic spin-Hall effect on the black hole horizon,” Phys. Rev. D 106 (2022) no.12, L121503 doi:10.1103/PhysRevD.106.L121503 [arXiv:2207.06302 [gr-qc]]

    2022 arXiv

  16. [24]

    Carrollian motion in magnetized black hole horizons,

    F. Gray, D. Kubiznak, T. R. Perche and J. Redondo-Yuste, “Carrollian motion in magnetized black hole horizons,” Phys. Rev. D107 (2023) no.6, 064009 doi:10.1103/PhysRevD.107.064009 [arXiv:2211.13695 [gr-qc]]

    2023 arXiv

  17. [25]

    Carroll-Hawking effect,

    A. Aggarwal, F. Ecker, D. Grumiller and D. Vassilevich, “Carroll-Hawking effect,” Phys. Rev. D 110 (2024) no.4, 4 doi:10.1103/PhysRevD.110.L041506 [arXiv:2403.00073 [hep-th]]

    2024 arXiv

  18. [26]

    Car- roll black holes,

    F. Ecker, D. Grumiller, J. Hartong, A. P´ erez, S. Prohazka and R. Troncoso, “Car- roll black holes,” SciPost Phys. 15 (2023) no.6, 245 doi:10.21468/SciPostPhys.15.6.245 [arXiv:2308.10947 [hep-th]]

    2023

  19. [27]

    Carroll swiftons,

    F. Ecker, D. Grumiller, M. Henneaux and P. Salgado-Rebolledo, “Carroll swiftons,” Phys. Rev. D 110 (2024) no.4, L041901 doi:10.1103/PhysRevD.110.L041901 [arXiv:2403.00544 [hep-th]]

    2024 arXiv

  20. [28]

    Hall effects in Carroll dynamics,

    L. Marsot, P. M. Zhang, M. Chernodub and P. A. Horvathy, “Hall effects in Carroll dynamics,” Phys. Rept. 1028 (2023), 1-60 doi:10.1016/j.physrep.2023.07.007 [arXiv:2212.02360 [hep-th]]

    2023 arXiv

  21. [29]

    Two interacting conformal Carroll particles,

    R. Casalbuoni, D. Dominici and J. Gomis, “Two interacting conformal Carroll particles,” Phys. Rev. D 108 (2023) no.8, 086005 doi:10.1103/PhysRevD.108.086005 [arXiv:2306.02614 24 [hep-th]]

    2023 arXiv

  22. [30]

    MultiCarroll dynamics,

    P. M. Zhang, H. X. Zeng and P. A. Horvathy, “MultiCarroll dynamics,” Int. J. Theor. Phys. (2024) [arXiv:2306.07002 [gr-qc]]

    2024 arXiv

  23. [31]

    The Effect of a Magnetic Field on Electrons in a Periodic Potential,

    J. Luttinger, “The Effect of a Magnetic Field on Electrons in a Periodic Potential,” Phys. Rev. 84 (1951) 814 DOI:10.1103/PhysRev.84.814

    1951 doi

  24. [32]

    Theory of Bloch Electrons in a Magnetic Field: The Effective Hamiltonian,

    W. Kohn, “Theory of Bloch Electrons in a Magnetic Field: The Effective Hamiltonian,” Phys. Rev. 115 (1959) 1460. doi:10.1103/PhysRev.115.1460

    1959 doi

  25. [33]

    Energy Spectrum of a Conduction Electron in a Magnetic Field,

    M. Azbel’, “Energy Spectrum of a Conduction Electron in a Magnetic Field,” Zh. Eksp. Teor. Fiz. 46, 939 (1964). [English translation: Sov. Phys. JETP 19, 634 (1964)]

    1964

  26. [34]

    Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,

    D. Hofstadter and R. Douglas, “Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,” Phys. Rev. B 14, 2239 (1976). doi:10.1103/PhysRevB.14.2239

    1976 doi

  27. [35]

    On the Theory of the Diamagnetism of Conduction Electrons,

    R. Peierls, “On the Theory of the Diamagnetism of Conduction Electrons,” Z. Phys. 80, 763 (1933). https://doi.org/10.1142/9789812795779−0010

    1933 doi

  28. [36]

    ‘Peierls substitution’ and Chern-Simons quantum mechanics,

    G. V. Dunne and R. Jackiw, “ ‘Peierls substitution’ and Chern-Simons quantum mechanics,” Nucl. Phys. B Proc. Suppl. 33 (1993), 114-118 doi:10.1016/0920-5632(93)90376-H [arXiv:hep- th/9204057 [hep-th]]

    1993

  29. [37]

    Topological (Chern-Simons) Quantum Mechanics,

    G. V. Dunne, R. Jackiw and C. A. Trugenberger, “Topological (Chern-Simons) Quantum Mechanics,” Phys. Rev. D 41 (1990), 661 doi:10.1103/PhysRevD.41.661

    1990 doi

  30. [38]

    The ‘Peierls substitution’ and the exotic Galilei group,

    C. Duval and P. A. Horvathy, “The ‘Peierls substitution’ and the exotic Galilei group,” Phys. Lett. B 479 (2000), 284-290 doi:10.1016/S0370-2693(00)00341-5 [arXiv:hep-th/0002233 [hep- th]]

    2000 arXiv

  31. [39]

    Brihaye, C

    Y. Brihaye, C. Gonera, S. Giller and P. Kosi´ nski, Galilean invariance in 2 + 1 dimensions. hep-th/9503046 (unpublished)

    arXiv

  32. [40]

    The projective unitary irreducible representations of the Galilei group in 1 + 2 dimensions,

    D. R. Grigore, “The projective unitary irreducible representations of the Galilei group in 1 + 2 dimensions,” Journ. Math. Phys. 37, 460; “Transitive symplectic manifolds in 1 + 2 dimensions,” 37 240 (1996)

    1996

  33. [41]

    Galilean-invariant (2 + 1)-dimensional models with a Chern-Simons-like term and d = 2 noncommutative geometry,

    J. Lukierski, P. C. Stichel, W. J. Zakrzewski, “Galilean-invariant (2 + 1)-dimensional models with a Chern-Simons-like term and d = 2 noncommutative geometry,” Annals of Physics (N. Y.) 260, 224 (1997)

    1997

  34. [42]

    (2+1)D Exotic Newton- Hooke Symmetry, Duality and Projective Phase,

    P. D. Alvarez, J. Gomis, K. Kamimura and M. S. Plyushchay, “(2+1)D Exotic Newton- Hooke Symmetry, Duality and Projective Phase,” Annals Phys. 322 (2007), 1556-1586 25 doi:10.1016/j.aop.2007.03.002 [arXiv:hep-th/0702014 [hep-th]]

    2007 arXiv

  35. [43]

    Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry,

    P. D. Alvarez, J. Gomis, K. Kamimura and M. S. Plyushchay, “Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry,” Phys. Lett. B 659 (2008), 906-912 doi:10.1016/j.physletb.2007.12.016 [arXiv:0711.2644 [hep-th]]

    2008 arXiv

  36. [44]

    Exotic Galilean symmetry in the noncommutative plane, and the Hall effect,

    C. Duval and P. A. Horvathy, “Exotic Galilean symmetry in the noncommutative plane, and the Hall effect,” J. Phys. A 34 (2001), 10097-10108 doi:10.1088/0305-4470/34/47/314 [arXiv:hep-th/0106089 [hep-th]]

    2001 arXiv

  37. [45]

    The Noncommutative Landau problem and the Peierls substitution,

    P. A. Horvathy, “The Noncommutative Landau problem and the Peierls substitution,” Annals Phys. 299 (2002), 128-140 doi:10.1006/aphy.2002.6271 [arXiv:hep-th/0201007 [hep-th]]

    2002

  38. [46]

    Exotic Galilean Symmetry and Non-Commutative Mechanics,

    P. A. Horvathy, L. Martina and P. C. Stichel, “Exotic Galilean Symmetry and Non-Commutative Mechanics,” SIGMA 6 (2010), 060 doi:10.3842/SIGMA.2010.060 [arXiv:1002.4772 [hep-th]]

    2010 arXiv

  39. [47]

    Chiral Decomposition in the Non-Commutative Landau Problem,

    P. M. Zhang and P. A. Horvathy, “Chiral Decomposition in the Non-Commutative Landau Problem,” Annals Phys. 327 (2012), 1730-1743 doi:10.1016/j.aop.2012.02.014 [arXiv:1112.0409 [hep-th]]

    2012 arXiv

  40. [48]

    Feynman integral for singular Lagrangians,

    L. D. Faddeev, “Feynman integral for singular Lagrangians,” Theor. Math. Phys. 1 (1969), 1-13 doi:10.1007/BF01028566

    1969 doi

  41. [49]

    Hamiltonian Reduction of Unconstrained and Constrained Systems,

    L. D. Faddeev and R. Jackiw, “Hamiltonian Reduction of Unconstrained and Constrained Systems,” Phys. Rev. Lett. 60 (1988), 1692-1694 doi:10.1103/PhysRevLett.60.1692

    1988 doi

  42. [50]

    Ezawa, The Quantum Hall Effects

    F. Ezawa, The Quantum Hall Effects. Field theoretical approach and related topics . World Scientific: Singapore (2000)

    2000

  43. [51]

    Stone, The Quantum Hall Effect

    M. Stone, The Quantum Hall Effect. Singapore: World Scientific (1992)

    1992

  44. [52]

    Hall Effect in Ferromagnetics,

    R. Karplus, J.M. Luttinger, “Hall Effect in Ferromagnetics,” Phys. Rev. 95 (1954) 1154

    1954

  45. [53]

    Anomalous Hall Effect in non-commutative mechanics,

    P. A. Horvathy, “Anomalous Hall Effect in non-commutative mechanics,” Phys. Lett. A 359 (2006) 705 [arXiv:cond-mat/0606472]

    2006 arXiv

  46. [54]

    Souriau, Structure des syst` emes dynamiques

    J.-M. Souriau, Structure des syst` emes dynamiques. Dunod (1970, © 1969); Structure of Dynamical Systems. A Symplectic View of Physics , translated by C.H. Cushman-de Vries (R.H. Cushman and G.M. Tuynman, Translation Editors), Birkh¨ auser, 1997

    1970

  47. [55]

    Kohn condition and exotic Newton-Hooke sym- metry in the non-commutative Landau problem,

    P. M. Zhang and P. A. Horvathy, “Kohn condition and exotic Newton-Hooke sym- metry in the non-commutative Landau problem,” Phys. Lett. B 706 (2012), 442-446 doi:10.1016/j.physletb.2011.11.035 [arXiv:1111.1595 [hep-th]]. 26

    2012 arXiv

  48. [56]

    Velocity Memory Effect for Polarized Gravitational Waves,

    P. M. Zhang, C. Duval, G. W. Gibbons and P. A. Horvathy, “Velocity Memory Effect for Polarized Gravitational Waves,” JCAP 05 (2018), 030 doi:10.1088/1475-7516/2018/05/030 [arXiv:1802.09061 [gr-qc]]

    2018 arXiv

  49. [57]

    On the coadjoint orbits of the planar Poincar´ e group,

    L. Feher, PhD thesis (1988) (in hungarian). An english summary is: “On the coadjoint orbits of the planar Poincar´ e group,” unpublished notes (2015)

    1988

  50. [58]

    The Fracton Gauge Principle,

    M. Pretko, “The Fracton Gauge Principle,” Phys. Rev. B 98 (2018) no.11, 115134 doi:10.1103/PhysRevB.98.115134 [arXiv:1807.11479 [cond-mat.str-el]]

    2018 arXiv

  51. [59]

    Fracton Phases of Matter,

    M. Pretko, X. Chen and Y. You, “Fracton Phases of Matter,” Int. J. Mod. Phys. A 35 (2020) no.06, 2030003 doi:10.1142/S0217751X20300033 [arXiv:2001.01722 [cond-mat.str-el]]

    2020 arXiv

  52. [60]

    Towards classification of Fracton phases: the multipole algebra,

    A. Gromov, “Towards classification of Fracton phases: the multipole algebra,” Phys. Rev. X 9 (2019) no.3, 031035 doi:10.1103/PhysRevX.9.031035 [arXiv:1812.05104 [cond-mat.str-el]]

    2019 arXiv

  53. [61]

    Field Theories With a Vector Global Symmetry,

    N. Seiberg, “Field Theories With a Vector Global Symmetry,” SciPost Phys. 8 (2020) no.4, 050 doi:10.21468/SciPostPhys.8.4.050 [arXiv:1909.10544 [cond-mat.str-el]]

    2020 arXiv

  54. [62]

    Fractons, dipole symmetries and curved spacetime,

    L. Bidussi, J. Hartong, E. Have, J. Musaeus and S. Prohazka, “Fractons, dipole symmetries and curved spacetime,” SciPost Phys. 12 (2022) no.6, 205 doi:10.21468/SciPostPhys.12.6.205 [arXiv:2111.03668 [hep-th]]

    2022 arXiv

  55. [63]

    Fractons in curved space,

    A. Jain and K. Jensen, “Fractons in curved space,” SciPost Phys. 12 (2022) no.4, 142 doi:10.21468/SciPostPhys.12.4.142 [arXiv:2111.03973 [hep-th]]

    2022 arXiv

  56. [64]

    Space-Dependent Sym- metries and Fractons,

    K. T. Grosvenor, C. Hoyos, F. Pe˜ na-Benitez and P. Sur´ owka, “Space-Dependent Sym- metries and Fractons,” Front. in Phys. 9 (2022), 792621 doi:10.3389/fphy.2021.792621 [arXiv:2112.00531 [hep-th]]

    2022

  57. [65]

    Hydrodynamics of dipole-conserving fluids,

    A. G l´ odkowski, F. Pe˜ na-Ben ´ ıtez and P. Sur´ owka, “Hydrodynamics of dipole-conserving fluids,” [arXiv:2212.06848 [cond-mat.str-el]]

    arXiv

  58. [66]

    Vortices and Fractons,

    D. Doshi and A. Gromov, “Vortices and Fractons,” [arXiv:2005.03015 [cond-mat.str-el]]

    2005 arXiv

  59. [67]

    Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,

    A. Bagchi, “Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,” Phys. Rev. Lett. 105 (2010) 171601

    2010

  60. [68]

    Conformal Carroll groups and BMS symmetry,

    C. Duval, G. W. Gibbons, P. A. Horvathy, “Conformal Carroll groups and BMS symmetry,” Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894 [gr-qc]]

    2014 arXiv

  61. [69]

    Carrollian superconformal theories and super BMS,

    A. Bagchi, D. Grumiller and P. Nandi, “Carrollian superconformal theories and super BMS,” JHEP 05 (2022), 044 doi:10.1007/JHEP05(2022)044 [arXiv:2202.01172 [hep-th]]

    2022 arXiv

  62. [70]

    Celestial holography: An asymptotic symmetry perspective,

    L. Donnay, “Celestial holography: An asymptotic symmetry perspective,” Phys. Rept. 1073 27 (2024), 1-41 doi:10.1016/j.physrep.2024.04.003 [arXiv:2310.12922 [hep-th]]

    2024 arXiv

  63. [71]

    Noncommuting coordinates in the Hall effect and in vortex dynamics,

    P. A. Horvathy, “Noncommuting coordinates in the Hall effect and in vortex dynamics,” [arXiv:hep-th/0307175 [hep-th]]

    arXiv

  64. [72]

    Carroll symmetry in vortex dynamics

    Zeng et al, “Carroll symmetry in vortex dynamics” (in preparation)

  65. [73]

    J-M Souriau retold once to one of us (PAH) that Galilei’s Gedankenexperiment was actually performed [74]

    https://en.wikipedia.org/wiki/Galilean −invariance: “Galileo Galilei first described this prin- ciple in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer belo...

  66. [74]

    According to https://gallica.bnf.fr/ark:/12148/bpt6k65697379 and https://fr.wikipedia.org/wiki/Pierre−Gassendi: “ M

    Pierre Gassendi (1592-1655) has carried out Galilei’s moving boat proposal in 1641 in Marseille harbour, De proportione qua gravia decidentia acceleren- tur (1646). According to https://gallica.bnf.fr/ark:/12148/bpt6k65697379 and https://fr.wikipedia.org/wiki/Pierre−Gassendi: ...

  67. [75]

    Iglesias-Zemmour, La g´ eom´ etrie des mouvements, Amazon KDP Publishing

    P. Iglesias-Zemmour, La g´ eom´ etrie des mouvements, Amazon KDP Publishing. ISBN 9781981032068 (2018). Appendix A: The Noether theorem in Souriau’s framework Here we summarise Souriau’s version of the Noether theorem, taken from chapter 12 of [54]. First we recall that a mech...

    2018

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.