G. A. Sardanashvily, “Classical Gauge Theory of Gravity”, TMF, 132:2 (2002), 318–328; Theoret. and Math. Phys., 132:2 (2002), 1163

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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 132, Number 2, Pages 318–328
DOI: https://doi.org/10.4213/tmf364 (Mi tmf364)

This article is cited in 27 scientific papers (total in 27 papers)

Classical Gauge Theory of Gravity

G. A. Sardanashvily

M. V. Lomonosov Moscow State University

Full-text PDF (208 kB) Citations (27)

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DOI: https://doi.org/10.4213/tmf364

Abstract: The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Reimannian metric (tetrad field) is the corresponding Higgs field. We consider two variants of this theory. In the first variant, gravity is represented by the pseudo-Reimannian metric as in general relativity theory; in the second variant, it is represented by the effective metric as in Logunov's relativistic theory of gravity. The configuration space, Dirac operator, and Lagrangians are constructed for both variants.

Keywords: gravity, gauge field, Higgs field, spinor field.

Received: 21.02.2002

English version:
Theoretical and Mathematical Physics, 2002, Volume 132, Issue 2, Pages 1163–1171
DOI: https://doi.org/10.1023/A:1019712911009

Bibliographic databases:

Language: Russian

Citation: G. A. Sardanashvily, “Classical Gauge Theory of Gravity”, TMF, 132:2 (2002), 318–328; Theoret. and Math. Phys., 132:2 (2002), 1163–1171

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf364

https://doi.org/10.4213/tmf364

https://www.mathnet.ru/eng/tmf/v132/i2/p318

This publication is cited in the following 27 articles:

Alcides Garat, “On the Nature of the New Group LB1”, Int J Theor Phys, 63:10 (2024)
Debono I., Smoot G.F., “General Relativity and Cosmology: Unsolved Questions and Future Directions”, Universe, 2:4 (2016), UNSP 23
Oikonomou V.K., “Localized Fermions on Domain Walls and Extended Supersymmetric Quantum Mechanics”, Class. Quantum Gravity, 31:2 (2014), 025018
G. A. Sardanashvily, “Classical Higgs fields”, Theoret. and Math. Phys., 181:3 (2014), 1599–1611
Capriotti S., “Differential Geometry, Palatini Gravity and Reduction”, J. Math. Phys., 55:1 (2014), 012902
Julve J. Tiemblo A., “A Perturbation Approach to Translational Gravity”, Int. J. Geom. Methods Mod. Phys., 10:10 (2013), 1350062
Oikonomou V.K., “Graded Geometric Structures Underlying F-Theory Related Defect Theories”, Int. J. Mod. Phys. A, 28:21 (2013)
Oikonomou V.K., “Hidden Supersymmetry in Dirac Fermion Quasinormal Modes of Black Holes”, Int. J. Mod. Phys. A, 28:15 (2013)
Pitts J.B., “The Nontriviality of Trivial General Covariance: How Electrons Restrict ‘Time’ Coordinates, Spinors (Almost) Fit Into Tensor Calculus, and 7/16 of a Tetrad Is Surplus Structure”, Stud. Hist. Philos. Mod. Phys., 43:1 (2012), 1–24
Malyshev C., “Non-singular screw dislocations as the Coulomb gas with smoothed-out coupling and the renormalization of the shear modulus”, J. Phys. A: Math. Theor., 44:28 (2011), 285003
Julve J., Tiemblo A., “Dynamical Variables in Gauge-Translational Gravity”, Int J Geom Methods Mod Phys, 8:2 (2011), 381–393
Martin-Martin J., Tiemblo A., “Gravity as a Gauge Theory of Translations”, International Journal of Geometric Methods in Modern Physics, 7:2 (2010), 323–335
Viennot D., “Holonomy of a principal composite bundle connection, non-Abelian geometric phases, and gauge theory of gravity”, J Math Phys, 51:10 (2010), 103501
Giachetta G., “On the notion of gauge symmetries of generic Lagrangian field theory”, Journal of Mathematical Physics, 50:1 (2009), 012903
Sardanashvily G., “Classical Field Theory. Advanced Mathematical Formulation”, International Journal of Geometric Methods in Modern Physics, 5:7 (2008), 1163
Sardanashvily G., “Mathematical models of spontaneous symmetry breaking - Preface”, International Journal of Geometric Methods in Modern Physics, 5:2 (2008), V-XVI
Aldaya V., “Gauge theories of gravity and mass generation”, International Journal of Geometric Methods in Modern Physics, 5:2 (2008), 197
Martin J., “The role of translational invariance in nonlinear gauge theories of gravity”, International Journal of Geometric Methods in Modern Physics, 5:2 (2008), 253
Sardanashvily G., “Supermetrics on supermanifolds”, International Journal of Geometric Methods in Modern Physics, 5:2 (2008), 271
“PREFACE”, Int. J. Geom. Methods Mod. Phys., 05:02 (2008), v

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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