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
- 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
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