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REVIEW 2 major objections 1 minor 68 references

The Diffeomorphism Field

T0 review · 2 major / 1 minor · reviewed 2026-05-24 · grok-4.3

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Pith's one-line read Dynamical theories for the diffeomorphism field in higher dimensions can be built by adapting the Kac-Moody construction of Yang-Mills theory, once subtleties in earlier attempts are resolved.

desk verdict This thesis carefully reviews and patches problems in earlier attempts to build a diffeomorphism field via Kac-Moody mimicry, but stays incremental with no first-principles advance. read the letter →

arxiv 1907.06766 v1 pith:K27QAODQ submitted 2019-07-15 math-ph math.MP

Delalcan Kilic This is my paper · ORCID
classification math-phmath.MP
keywords diffeomorphismfieldVirasoroalgebracoadjointorbitsYang-MillstheoryKac-Moodyalgebrastwo-dimensionalgravityhigher-dimensionalextensions
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

The paper starts from the two-dimensional case where integration of the Kirillov form on a Virasoro coadjoint orbit produces a background field that couples to Polyakov gravity and can be viewed as a gravitational analog of a Yang-Mills field. It then asks whether this diffeomorphism field can be given its own consistent dynamics in dimensions greater than two. Several prior constructions that copy the structure of Yang-Mills theory are examined in detail. Problems and inconsistencies are identified, some are corrected, routes are suggested for the remainder, and alternative geometric methods are explored.

What carries the argument

The direct structural analogy between the diffeomorphism field and Yang-Mills fields derived from Kac-Moody algebras, used to generate candidate actions and equations of motion in higher dimensions.

What would settle it

Explicit derivation of the equations of motion from one of the proposed higher-dimensional actions, followed by a check that shows either internal inconsistency or failure to recover the known two-dimensional coupling when restricted to two dimensions.

Watch

Extended reading notes

Core claim

The diffeomorphism field, originally obtained from the Virasoro algebra in two dimensions, admits a consistent dynamical extension to higher dimensions when the equations are written by direct analogy with Yang-Mills theory from Kac-Moody algebras, provided that the subtleties and problems present in previous proposals are identified and addressed.

Load-bearing premise

That the diffeomorphism field admits a consistent dynamical extension to higher dimensions whose equations are obtained simply by copying the structure of Yang-Mills theory from Kac-Moody algebras.

Editorial extensions

If this is right

  • Consistent equations of motion for the diffeomorphism field become available in dimensions greater than two once identified problems are fixed.
  • The field can be treated as an independent dynamical entity rather than a pure background in higher-dimensional gravity models.
  • Alternative geometric constructions provide an independent route to the same dynamical theories.
  • Some of the earlier proposals can be salvaged with targeted corrections.

Reading between the lines

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

  • If the construction succeeds, the diffeomorphism field could play a structural role in higher-dimensional gravity comparable to the role Yang-Mills fields play in gauge theory.
  • The same analogy might suggest how to incorporate the field into quantization procedures that already work for Yang-Mills theory.
  • Failure to find a consistent extension would indicate that the two-dimensional construction does not generalize in a simple copy-and-paste manner.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript examines prior proposals for dynamical theories of the diffeomorphism field in higher dimensions, constructed by mimicking the Kac-Moody algebra route to Yang-Mills theory. It identifies subtleties and problems in these constructions, resolves some of them, outlines possible routes for the remainder, and investigates alternative geometric approaches. The work is motivated by the two-dimensional case where the diffeomorphism field arises from integration of the Kirillov form on Virasoro coadjoint orbits and is interpreted as a gravitational analog of a Yang-Mills field.

Significance. If the resolutions of the identified subtleties prove consistent and non-circular, the thesis would advance the program of constructing a higher-dimensional dynamical theory for the diffeomorphism field, potentially clarifying its role in gravity beyond two dimensions. The explicit identification of problems in prior work and exploration of alternatives constitute a useful incremental contribution, though the absence of explicit new equations or derivations in the abstract limits immediate assessment of novelty.

major comments (2)
  1. [Abstract, motivation and construction paragraph] The central construction method relies on 'mimicking' the Kac-Moody/Yang-Mills route, yet no explicit comparison of the resulting equations to existing structures is supplied to rule out reduction to relabeling; this bears directly on whether the higher-dimensional extension is independent.
  2. [Sections describing examination of prior theories] The claim that certain subtleties have been solved requires verification against the original proposals; without displayed derivations or counter-examples in the examined sections, it is impossible to confirm that the resolutions are load-bearing and non-circular.
minor comments (1)
  1. Notation for the diffeomorphism field and its coupling should be standardized across sections to avoid confusion with Virasoro generators.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these points regarding the construction and verification of the results. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract, motivation and construction paragraph] The central construction method relies on 'mimicking' the Kac-Moody/Yang-Mills route, yet no explicit comparison of the resulting equations to existing structures is supplied to rule out reduction to relabeling; this bears directly on whether the higher-dimensional extension is independent.

    Authors: We agree that an explicit comparison of the resulting equations with standard Yang-Mills and diffeomorphism structures would strengthen the argument for independence of the higher-dimensional extension. The mimicking procedure is constructed to yield a distinct dynamical theory due to the properties of the infinite-dimensional algebra, but the manuscript does not currently include a direct side-by-side analysis. We will add such a comparison in a revised version to address this concern. revision: yes

  2. Referee: [Sections describing examination of prior theories] The claim that certain subtleties have been solved requires verification against the original proposals; without displayed derivations or counter-examples in the examined sections, it is impossible to confirm that the resolutions are load-bearing and non-circular.

    Authors: The manuscript identifies subtleties in prior constructions and outlines resolutions for some of them. We acknowledge that the current presentation does not always include full derivations or counter-examples sufficient for independent verification of non-circularity. In the revised manuscript we will expand the relevant sections to display the key derivations and counter-examples explicitly. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The thesis describes prior constructions of dynamical theories for the diffeomorphism field obtained by mimicking the Kac-Moody/Yang-Mills route from 2D Virasoro coadjoint orbits, then states that it examines those proposals, identifies subtleties and problems, solves some, outlines routes for others, and investigates alternative geometric approaches. No load-bearing derivation, equation, or uniqueness claim is exhibited that reduces by construction to a fitted input, self-citation chain, or renamed ansatz; the central activity is analysis and partial resolution rather than a first-principles prediction whose output equals its input. The work is therefore self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 2 assumptions · 1 invented entities

The central claim rests on the premise that a diffeomorphism field defined in 2D via Virasoro orbits extends consistently to higher dimensions when its dynamics are copied from Kac-Moody Yang-Mills; this premise is not independently evidenced in the abstract.

assumptions (2)
  • domain assumption Einstein's gravity is dynamically trivial in two dimensions
    Stated directly in the abstract as background fact used to motivate the diffeomorphism field.
  • domain assumption The diffeomorphism field can be interpreted as the gravitational analog of a Yang-Mills field
    Abstract asserts this interpretation without derivation.
invented entities (1)
  • diffeomorphism field
    purpose: Background field coupling to 2D quantum gravity that is extended to a dynamical field in higher dimensions
    Introduced via Kirillov form on Virasoro coadjoint orbit; no independent evidence supplied in abstract.

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Cite this review

Pith. "Pith review of The Diffeomorphism Field." pith.science (2026). https://pith.science/paper/K27QAODQ

@misc{pith2026190706766,
  author       = {Pith},
  title        = {Pith review of: The Diffeomorphism Field},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K27QAODQ}},
  note         = {Machine review of arXiv:1907.06766}
}
read the original abstract

Integration of Kirillov form on a coadjoint orbit of Virasoro algebra yields the coupling of a background field to Polyakov's two dimensional quantum gravity. This background field is used to be called the diffeomorphism field. Einstein's gravity is dynamically trivial in two dimensions. Moreover, the diffeomorphism field can be interpreted as the gravitational analog of a Yang-Mills field. This raises the question of whether the diffeomorphism field exists in higher dimensions, and plays an essential role in gravity. With this motivation, several dynamical theories for the diffeomorphism field have been constructed by mimicking construction of Yang-Mills theory from Kac-Moody algebra. This thesis constitutes a further development for obtaining a consistent dynamical theory of the diffeomorphism field. The previously proposed theories are thoroughly examined, certain subtleties and problems in them have been discovered and made apparent. Some of these problems have been solved, and for others possible routes to follow have been laid down. Finally, alternative geometric approaches are investigated.

Figures

Figures reproduced from arXiv: 1907.06766 by the authors.

Figure 2.1
Figure 2.1. The Two-surface m Traced by the Paths [PITH_FULL_IMAGE:figures/full_fig_p027_2_1.png] view at source ↗
Figure 4.1
Figure 4.1. Geometric vs Transverse Actions [PITH_FULL_IMAGE:figures/full_fig_p073_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Yang-Mills vs Diff Field - Structure Comparison [PITH_FULL_IMAGE:figures/full_fig_p090_4_2.png] view at source ↗

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Works this paper leans on

68 extracted references · 68 canonical work pages

  1. [1]

    From coadjoint orbits to scale invariant wznw type actions and 2d quantum gravity action

    Balram Rai and VGJ Rodgers. From coadjoint orbits to scale invariant wznw type actions and 2d quantum gravity action. Nuclear Physics B, 341(1):119–133, 1990

    work page 1990

  2. [2]

    A study of fermions coupled to gauge and gravitational fields on a cylinder

    Ralph P Lano and VGJ Rodgers. A study of fermions coupled to gauge and gravitational fields on a cylinder. Nuclear Physics B , 437(1):45–59, 1995

    work page 1995

  3. [3]

    Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity

    A Alekseev and S Shatashvili. Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity. Nuclear Physics B , 323(3):719–733, 1989

    work page 1989

  4. [4]

    Non-abelian bosonization in two dimensions

    Edward Witten. Non-abelian bosonization in two dimensions. Communications in Mathematical Physics , 92(4):455–472, 1984

    work page 1984

  5. [5]

    Quantum gravity in two dimensions

    Alexander M Polyakov. Quantum gravity in two dimensions. Modern Physics Letters A, 2(11):893–898, 1987

    work page 1987

  6. [6]

    The wess–zumino action in two dimensions and non-abelian bosonization

    P Di Vecchia, B Durhuus, and JL Petersen. The wess–zumino action in two dimensions and non-abelian bosonization. In Bosonization, pages 224–228. World Scientific, 1994

    work page 1994

  7. [7]

    Two-dimensional non-abelian bosoniza- tion in the presence of external gauge fields and gravity

    AN Redlich and Howard J Schnitzer. Two-dimensional non-abelian bosoniza- tion in the presence of external gauge fields and gravity. Physics Letters B , 193(4):471–475, 1987

    work page 1987

  8. [8]

    Fractal structure of 2d—quantum gravity

    Vadim G Knizhnik, Alexander M Polyakov, and Alexander B Zamolodchikov. Fractal structure of 2d—quantum gravity. Modern Physics Letters A, 3(08):819– 826, 1988

    work page 1988

Show all 68 references
  1. [9]

    Quantum geometry of bosonic strings

    Alexander M Polyakov. Quantum geometry of bosonic strings. Physics Letters B, 103(3):207–210, 1981

    1981

  2. [10]

    Quantum gravity on a circle and the diffeomor- phism invariance of the schr¨ odinger equation

    RJ Henderson and SG Rajeev. Quantum gravity on a circle and the diffeomor- phism invariance of the schr¨ odinger equation. Classical and Quantum Gravity , 11(7):1631, 1994

    1994

  3. [11]

    Quantum gravity : variations on a theme

    Ralph P Lano. Quantum gravity : variations on a theme . PhD thesis, University of Iowa, 1996

    1996

  4. [12]

    A 2d inspired 4d theory of gravity

    VGJ Rodgers. A 2d inspired 4d theory of gravity. Physics Letters B , 336(3- 4):343–346, 1994. 201

    1994

  5. [13]

    Yang-mills theory on a cylinder

    SG Rajeev. Yang-mills theory on a cylinder. Physics Letters B, 212(2):203–205, 1988

    1988

  6. [14]

    Yang-mills, gravity, and 2d string symmetries

    RP Lano and VGJ Rodgers. Yang-mills, gravity, and 2d string symmetries. Technical report, 1996

    1996

  7. [15]

    Yang-mills, gravity, and string symmetries

    Thomas Branson, RP Lano, and VGJ Rodgers. Yang-mills, gravity, and string symmetries. Physics Letters B , 412(3):253–258, 1997

    1997

  8. [16]

    Interactions of a string inspired graviton field

    Thomas P Branson, VGJ Rodgers, and Takeshi Yasuda. Interactions of a string inspired graviton field. International Journal of Modern Physics A , 15(22):3549– 3562, 2000

    2000

  9. [17]

    General coordinate transformations as the origins of dark energy

    Vincent GJ Rodgers and Takeshi Yasuda. General coordinate transformations as the origins of dark energy. International Journal of Modern Physics A , 22(04):749–776, 2007

    2007

  10. [18]

    The cosmological implications of diffeomorphisms

    Takeshi Yasuda. The cosmological implications of diffeomorphisms . 2006

    2006

  11. [19]

    Supergravitons interacting with the super- virasoro group

    S James Gates and VGJ Rodgers. Supergravitons interacting with the super- virasoro group. Physics Letters B , 512(1):189–196, 2001

    2001

  12. [20]

    Covariant differential operators for densities and the kdv equation as a flow on diffeomorphism groups

    Wolfgang Scherer. Covariant differential operators for densities and the kdv equation as a flow on diffeomorphism groups. letters in mathematical physics , 17(1):45–49, 1989

    1989

  13. [21]

    Dynamical projective curvature in gravitation

    Samuel Brensinger and Vincent GJ Rodgers. Dynamical projective curvature in gravitation. arXiv preprint arXiv:1712.05394 , 2017

    2017 arXiv

  14. [22]

    Lectures on the orbit method , volume 64

    Aleksandr Aleksandrovich Kirillov. Lectures on the orbit method , volume 64. American Mathematical Soc., 2004

    2004

  15. [23]

    Coadjoint orbits of the virasoro group

    Edward Witten. Coadjoint orbits of the virasoro group. Communications in Mathematical Physics, 114(1):1–53, 1988

    1988

  16. [24]

    Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems , volume 17

    Jerrold E Marsden and Tudor Ratiu. Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems , volume 17. Springer Science & Business Media, 2013

    2013

  17. [25]

    Universal unfolding of hamiltonian systems: From symplectic struc- ture to fiber bundles

    F Zaccaria, ECG Sudarshan, JS Nilsson, N Mukunda, G Marmo, and AP Bal- achandran. Universal unfolding of hamiltonian systems: From symplectic struc- ture to fiber bundles. Physical Review D, 27(10):2327, 1983. 202

    1983

  18. [26]

    Gauge symmetries and fibre bundles: applications to particle dynamics

    Aiyalam P Balachandran, Giuseppe Marmo, B-S Skagerstam, and A Stern. Gauge symmetries and fibre bundles: applications to particle dynamics. InGauge Symmetries and Fibre Bundles: Applications to Particle Dynamics , volume 188, 1983

    1983

  19. [27]

    Kac-moody and virasoro algebras in relation to quantum physics

    Peter Goddard and David Olive. Kac-moody and virasoro algebras in relation to quantum physics. International Journal of Modern Physics A , 1(02):303–414, 1986

    1986

  20. [28]

    The method of coadjoint orbits: An algorithm for the construction of invariant actions

    Gustav W Delius, Peter van Nieuwenhuizen, and VGJ Rodgers. The method of coadjoint orbits: An algorithm for the construction of invariant actions. Inter- national Journal of Modern Physics A , 5(20):3943–3983, 1990

    1990

  21. [29]

    A geometric action for the courant bracket.arXiv preprint hep-th/0610021, 2006

    Xiaolong Liu, Leopoldo A Pando Zayas, Vincent GJ Rodgers, and Leo Rodriguez. A geometric action for the courant bracket.arXiv preprint hep-th/0610021, 2006

    2006 arXiv

  22. [30]

    The cohomology of the lie algebra of vector fields on a circle

    IM Gelfand. The cohomology of the lie algebra of vector fields on a circle. Functs. Anal. Prirozhen, 2, 1968

    1968

  23. [31]

    Cambridge University Press, 2006

    Katrin Becker, Melanie Becker, and John H Schwarz.String theory and M-theory: A modern introduction. Cambridge University Press, 2006

    2006

  24. [32]

    Projective differential geometry old and new: from the Schwarzian derivative to the cohomology of diffeomorphism groups, volume 165

    Valentin Ovsienko and Serge Tabachnikov. Projective differential geometry old and new: from the Schwarzian derivative to the cohomology of diffeomorphism groups, volume 165. Cambridge University Press, 2004

    2004

  25. [33]

    G. Segal. Loop groups

  26. [34]

    Applications of w algebras to bf theories, qcd and 4d gravity

    Ralph Peter Lano and VGJ Rodgers. Applications of w algebras to bf theories, qcd and 4d gravity. Modern Physics Letters A , 7(19):1725–1736, 1992

    1992

  27. [35]

    Theory of nonabelian goldstone bosons in two dimensions

    A Polyakov and Paul B Wiegmann. Theory of nonabelian goldstone bosons in two dimensions. Physics Letters B , 131(1):121–126, 1983

    1983

  28. [36]

    Goldstone fields in two dimensions with multivalued actions

    Alexander M Polyakov and PB Wiegmann. Goldstone fields in two dimensions with multivalued actions. Physics Letters B , 141(3-4):223–228, 1984

    1984

  29. [37]

    Axial-vector vertex in spinor electrodynamics

    Stephen L Adler. Axial-vector vertex in spinor electrodynamics. Physical Review, 177(5):2426, 1969

    1969

  30. [38]

    Nuovo cimento a, 60, 47 (1969)

    JS Bell and R Jackiw. Nuovo cimento a, 60, 47 (1969). CrossRef ADS Google Scholar, 1963

    1969

  31. [39]

    Lectures on anomalies

    Adel Bilal. Lectures on anomalies. arXiv preprint arXiv:0802.0634 , 2008. 203

    2008 arXiv

  32. [40]

    Path-integral measure for gauge-invariant fermion theories

    Kazuo Fujikawa. Path-integral measure for gauge-invariant fermion theories. Physical Review Letters, 42(18):1195, 1979

    1979

  33. [41]

    Quantum field theory

    V Parameswaran Nair. Quantum field theory. Quantum Field Theory: A Modern Perspective, Graduate Texts in Contemporary Physics. ISBN 978-0-387-21386-6. Springer Science+ Business Media, Inc., 2005 , 1, 2005

    2005

  34. [42]

    Quantum sine-gordon equation as the massive thirring model, 1975 phys

    S Coleman. Quantum sine-gordon equation as the massive thirring model, 1975 phys. Rev. D, 11:2088

    1975

  35. [43]

    Soliton operators for the quantized sine-gordon equation

    S Mandelslam. Soliton operators for the quantized sine-gordon equation. In Bosonization, pages 138–142. World Scientific, 1994

    1994

  36. [44]

    Two-dimensional quantum gravity: Superconductivity at high t/c

    Alexander M Polyakov. Two-dimensional quantum gravity: Superconductivity at high t/c. 1988

    1988

  37. [45]

    Geometry, topology and physics

    Mikio Nakahara. Geometry, topology and physics . CRC Press, 2003

    2003

  38. [46]

    Conformal field theory

    Sergei V Ketov. Conformal field theory . World Scientific, 1995

    1995

  39. [47]

    Superstring theory, vols i and ii, 1987

    MB Green, JH Schwarz, and E Witten. Superstring theory, vols i and ii, 1987

    1987

  40. [48]

    Gravitation

    Charles W Misner, Kip S Thorne, and John Archibald Wheeler. Gravitation. Princeton University Press, 2017

    2017

  41. [49]

    A note on lie-lorentz derivatives

    Y Kosmann. A note on lie-lorentz derivatives. Annali di Mat. Pura Appl , 1972

    1972

  42. [50]

    On non-abelian generalisation of the born-infeld action in string theory

    Arkady A Tseytlin. On non-abelian generalisation of the born-infeld action in string theory. Nuclear Physics B , 501(1):41–52, 1997

    1997

  43. [51]

    Fermions without vierbeins in curved space-time

    H Arthur Weldon. Fermions without vierbeins in curved space-time. Physical Review D, 63(10):104010, 2001

    2001

  44. [52]

    Conformal invariance, supersymmetry and string theory

    Daniel Friedan, Emil Martinec, and Stephen Shenker. Conformal invariance, supersymmetry and string theory. Nuclear Physics B , 271(1):93–165, 1986

    1986

  45. [53]

    Canonical gravity and applications: cosmology, black holes, and quantum gravity

    Martin Bojowald. Canonical gravity and applications: cosmology, black holes, and quantum gravity . Cambridge University Press, 2010

    2010

  46. [54]

    Lectures on quantum mechanics

    Paul AM Dirac. Lectures on quantum mechanics . Courier Dover Publications, 2013

    2013

  47. [55]

    The euler-poincar´ e equations and double bracket dissipation

    Anthony Bloch, PS Krishnaprasad, Jerrold E Marsden, and Tudor S Ratiu. The euler-poincar´ e equations and double bracket dissipation. Communications in mathematical physics, 175(1):1–42, 1996. 204

    1996

  48. [56]

    Funkt, anal i ego prilozh 9, 75 (1975); e

    VF Lazutkin and TF Pankratova. Funkt, anal i ego prilozh 9, 75 (1975); e. witten. Comm, Math. Phys , 114:1, 1988

    1975

  49. [57]

    Unitary representations of some infinite dimensional groups.Com- munications in Mathematical Physics , 80(3):301–342, 1981

    Graeme Segal. Unitary representations of some infinite dimensional groups.Com- munications in Mathematical Physics , 80(3):301–342, 1981

    1981

  50. [58]

    On the projective and equi-projective geometries of paths

    Tracy Yerkes Thomas. On the projective and equi-projective geometries of paths. Proceedings of the National Academy of Sciences , 11(4):199–203, 1925

    1925

  51. [59]

    A projective theory of affinely connected manifolds.Math- ematische Zeitschrift, 25(1):723–733, 1926

    Tracy Yerkes Thomas. A projective theory of affinely connected manifolds.Math- ematische Zeitschrift, 25(1):723–733, 1926

    1926

  52. [60]

    The representation of projective spaces

    John Henry Constantine Whitehead. The representation of projective spaces. Annals of Mathematics , pages 327–360, 1931

    1931

  53. [61]

    Projective connections

    Michael Crampin and DJ Saunders. Projective connections. Journal of Geometry and Physics, 57(2):691–727, 2007

    2007

  54. [62]

    The projective connections of ty thomas and jhc whitehead applied to invariant connections

    Craig W Roberts. The projective connections of ty thomas and jhc whitehead applied to invariant connections. Differential Geometry and its Applications , 5(3):237–255, 1995

    1995

  55. [63]

    Infinite dimensional lie groups; their orbits, invariants and represen- tations

    AA Kirillov. Infinite dimensional lie groups; their orbits, invariants and represen- tations. the geometry of moments. In Twistor geometry and non-linear systems , pages 101–123. Springer, 1982

    1982

  56. [64]

    Projectively invariant objects and the index of the group of affine transformations in the group of projective transformations

    Vladimir S Matveev. Projectively invariant objects and the index of the group of affine transformations in the group of projective transformations. arXiv preprint arXiv:1604.01238, 2016

    2016

  57. [65]

    Sulle trasformazioni delle equazioni dinamiche

    Tullio Levi-Civita. Sulle trasformazioni delle equazioni dinamiche. Annali di Matematica Pura ed Applicata (1867-1897) , 24(1):255–300, 1896

  58. [66]

    Quantization of gauge systems

    Marc Henneaux and Claudio Teitelboim. Quantization of gauge systems . Prince- ton university press, 1992

    1992

  59. [67]

    The theorem of ostrogradsky

    Richard P Woodard. The theorem of ostrogradsky. arXiv preprint arXiv:1506.02210, 2015

    2015 arXiv

  60. [68]

    Ostrogradski’s theorem for higher-order singular lagrangians

    JM Pons. Ostrogradski’s theorem for higher-order singular lagrangians. letters in mathematical physics , 17(3):181–189, 1989

    1989

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