Higher Symplectic Gravity

Higher Symplectic Gravity (HSG)

Application of Higher Geometry - in particular mupo geometry (mupo for multisymplectic-polysymplectic) - to gravitation theory. Emergence of the idea that HSG is the adequate background towards a quantum theory of gravity.

  • Emergence of curved space-times by crystallization.
  • Classification of Observable forms and Algebraic observable forms in 4-plectic and 10-plectic Gravity.
  • Higher gauge theory and crystallization.

Curved space-times by Crystallization

Cycle of Conferences 2015—2016

Cycle of conferences related to Hamiltonian formalism, Higher symplectic geometry and Gravity

  • June 10, 2016 — Paris, France — Cristallisation de connexions et de fibrés liquides
    [F. Hélein, Paris 7, IMG—PRG] Séminaire de Géométrie et Quantification organisé par: Pierre Cartier, Yvette Kosmann-Schwarzbach, Camille Laurent-Gengoux IHP (Institute Henri Poincaré),
  • April 1, 2016 — Paris, France — Cristallisation de connexions et de fibrés liquides
    Département de Mathématiques, D. Diderot University, Paris 7. [F. Hélein, Paris 7, IMG—PRG]
  • August 21, 2015 — Stará Lesná, Slovakia — Generalized Hamiltonian Gravity: 10-plectic formulation of vierbein gravity
    Lepage Institute, contribution to: 20th International Summer School on Global Analysis and its Applications: General Relativity: 100 years after Hilbert. [D. Vey — NIQG]
    Slides Direct link [NWI] slides — Research Gate link [RG] slides
  • August 4, 2015 — Bogotá, Colombia — m-plectic formulation of n-bein gravity
    Universidad Nacional, Departamento de Mathemáticas — [D. Vey, NIQG]
  • August 3, 2015 — Bogotá, Colombia — Observables and brackets in the Hamiltonian formulation of physical theories
    Departamento de Física, Universidad de los Andes. [D. Vey, NIQG]
    Slides Direct link [NWI] slides — Research Gate link [RG] slides list of related references
  • July 27, 2015 — Villa de Leyva, Colombia — Hamiltonian Covariant formalism and higher symplectic geometry
    Universidad de los Andes, contribution to the summer school: Geometric, Algebraic and topological methods for Quantum Field Theory— [D. Vey, NIQG]
  • June 11, 2015 — Paris, France — Formulation multisymplectique de la vierbein gravity
    Université D. Diderot, Paris 7 — [D. Vey — NIQG]

Basic References

Einstein—Hilbert Gravity

  • M. Castrillón López, J. Muoz Masqué and E. Rosado María, First-order equivalent to Einstein-Hilbert Lagrangian.
    J. Math. Phys. 5 (2014), 082501, pp. 1–9. — doi: doi.org/10.1063/1.4890555 — arXiv arXiv:1306.1123v1
  • J. Gaset, P.D. Prieto-Martínez and N. Román-Roy, Variational principles and symmetries on fibered multisymplectic manifolds,
    DGDSA-MAT-UPC 2016 (1) — arXiv arXiv:1610.08689v2
  • E. Rosado María and J. Muoz Masqué, Second-order Lagrangians admitting a first-order Hamiltonian formalism,
    arXiv arXiv:1509.01037v1
  • E. Rosado María and J. Muoz Masqué, Integrability of second-order Lagrangians admitting a first-order Hamiltonian formalism,
    Diff. Geom. and Apps. 35, 164-177 (2014)

Einstein—Cartan Gravity

  • F. Hélein and D. Vey, Curved space-times by crystallization of liquid fiber bundles.
    Foundations of Physics 47(1):1-41, 2017 — doi: doi:10.1007/s10701-016-0039-2 — arXiv arXiv:1508.07765
  • A Ibort and A. Spivak On A Covariant Hamiltonian Description of Palatini's Gravity on Manifolds with Boundary,
    arXiv arXiv:1605.03492
  • S. Nakajima, Application of covariant analytic mechanics with differential forms to gravity with Dirac field,
    EJTP 13, 95 (2016) arXiv arXiv:1510.09048v2
  • M. Pilc, Covariant Quantum Gravity with Continuous Quantum Geometry I: Covariant Hamiltonian Framework,
    arXiv arXiv:1609.08021v1
  • D. Vey, 10–plectic formulation of gravity and Cartan connections,
    pre-publication (2016) hal hal-01408289v2
  • D. Vey, Generalized Hamiltonian Gravity,
    RG doi:10.13140/RG.2.1.3953.2401. also in: D. Krupka et al. (eds.), Extended Abstract Book, 20th International Summer School on Global Analysis and its Applications, Stara Lesna, Slovakia, August 17-21, University of Presov (2015).
  • D. Vey, Multisymplectic Formulation of Vielbein Gravity I. De Donder-Weyl Formulation, Hamiltonian (n-1)-forms,
    Class. Quantum Grav. 32 095005 (2015) arXiv arXiv:1404.3546v4
  • Y. Kaminaga, Covariant Analytic Mechanics with Differential Forms and Its Application to Gravity,
    EJTP 9, No. 26 (2012) 199–216. arXiv ejtpv9i26p199.pdf
  • D. Bruno, R. Cianci and S. Vignolo, A first-order purely frame formulation of General Relativity,
    Class.Quant.Grav. 22 4063-4070 arXiv arXiv:math-ph/0506077v1
  • D. Bruno, R. Cianci and S. Vignolo, General Relativity as a constrained Gauge Theory,
    Int.J.Geom.Meth.Mod.Phys. 3 (2006) 1493-1500 arXiv https://arxiv.org/abs/math-ph/0605059v1
  • C. Rovelli, A note on the foundation of relativistic mechanics — II: Covariant Hamiltonian general relativity,
    arXiv arXiv:gr-qc/0202079v1
  • G. Esposito, G. Gionti and C. Stornaiolo, Space-time covariant form of Ashtekar constraints,
    Nuovo Cim.B110:1137-1152,1995 arXiv arXiv:gr-qc/9506008

MacDowell-Mansouri Gravity

  • J. Berra-Montiel, A. Molgado and D. Serrano-Blanco, Covariant Hamiltonian formulation for MacDowell-Mansouri gravity,
    arXiv arXiv:1703.09755v1

Precanonical Quantum Gravity

  • I.V. Kanatchikov, Ehrenfest Theorem in Precanonical Quantization of Fields and Gravity,
    arXiv arXiv:1602.01083v1
  • I.V. Kanatchikov, De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity,
    J. Phys.: Conf. Ser. 442 012041 (2013) arXiv arXiv:1302.2610v2
  • I.V. Kanatchikov, On precanonical quantization of gravity in spin connection variables,
    AIP Conf.Proc. 1514 (2012) 73-76 arXiv arXiv:1212.6963v4
  • I.V. Kanatchikov, Precanonical Quantum Gravity: quantization without the space-time decomposition,
    Int.J.Theor.Phys.40:1121-1149,2001 arXiv arXiv:gr-qc/0012074v2