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TMF, 1974,	Volume 21,	Number 3,	Pages 329–342	(Mi tmf3902)
This article is cited in 26 scientific papers (total in 26 papers)
Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
A. B. Borisov, V. I. Ogievetskii
Abstract: Invariance under the infinite-parameter generally covariant group is equivalent to simultaneous invariance under the affine and the conformal group. A nonlinear realization of the affine group (with linearization on the poincar6 group) leads to a symmetric tensor field as Goldstone field. The requirement that the theory correspond simultaneously to a realization of the conformal group as well leads uniquely to the theory of a tensor field whose equations are Einstein's. This shows that the theory of the gravitational field is the theory of spontaneous breaking of affine and conformal symmetries in the same way as chiral dynamics is the theory of spontaneous breaking of chiral symmetry. This analogy brings out new aspects of the role of gravitation in the theory of elementary particles.
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Theoretical and Mathematical Physics, 1974, 21:3, 1179–1188
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Received: 29.12.1973
Citation: A. B. Borisov, V. I. Ogievetskii, "Theory of dynamical affine and conformal symmetries as the theory of the gravitational field", TMF, 21:3 (1974), 329–342; Theoret. and Math. Phys., 21:3 (1974), 1179–1188
Citation in format AMSBIB
\Bibitem{BorOgi74}
\by A.~B.~Borisov, V.~I.~Ogievetskii
\paper Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
\jour TMF
\pages 329--342
\mathnet{http://mi.mathnet.ru/tmf3902}
\jour Theoret. and Math. Phys.
\pages 1179--1188
\crossref{https://doi.org/10.1007/BF01038096}
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http://mi.mathnet.ru/eng/tmf3902
http://mi.mathnet.ru/eng/tmf/v21/i3/p329
This publication is cited in the following articles:
E. A. Ivanov, V. I. Ogievetskii, "Inverse Higgs effect in nonlinear realizations", Theoret. and Math. Phys., 25:2 (1975), 1050–1059
E. A. Ivanov, "On $\Sigma$ models of spontane ously broken symmetries", Theoret. and Math. Phys., 28:3 (1976), 814–821
V. N. Pervushin, "Dynamical affine symmetry and covariant perturbation theory for gravitation", Theoret. and Math. Phys., 27:1 (1976), 302–306
A. B. Borisov, "Unitary representations of the algebra of the general covariance group", Theoret. and Math. Phys., 33:3 (1977), 1116–1118
N. G. Pletnev, "Linear supergravity", Theoret. and Math. Phys., 43:1 (1980), 313–318
V. P. Akulov, I. A. Bandos, V. G. Zima, "Nonlinear realization of extended superconformal symmetry", Theoret. and Math. Phys., 56:1 (1983), 635–642
N. G. Pletnev, V. V. Serebryakov, "Covariant formalism of reductions of superconformal gauge theories to Poincaré supergravities", Theoret. and Math. Phys., 70:2 (1987), 179–186
E. A. Ivanov, "Conformal Theories–A{d}S Branes Transform, or One More Face of A{d}S/CFT", Theoret. and Math. Phys., 139:1 (2004), 513–528
Ivanov, EA, "AdS branes from partial breaking of superconformal symmetries", Physics of Atomic Nuclei, 68:10 (2005), 1713
Ivanov, E, "Higher spins from non-linear realizations of OSp(1 vertical bar 8)", Physics Letters B, 624:3–4 (2005), 304
Tiemblo, A, "Gravitational contribution to fermion masses", European Physical Journal C, 42:4 (2005), 437
Alexei J. Nurmagambetov, "Duality-Symmetric Approach to General Relativity and Supergravity", SIGMA, 2 (2006), 020, 34 pp.
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Leclerc, M, "The Higgs sector of gravitational gauge theories", Annals of Physics, 321:3 (2006), 708
West, P, "E-11 and higher spin theories", Physics Letters B, 650:2–3 (2007), 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
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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
McArthur I.N., "Nonlinear realizations of symmetries and unphysical Goldstone bosons", Journal of High Energy Physics, 2010, no. 11, 140
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Julve J., Tiemblo A., "Dynamical Variables in Gauge-Translational Gravity", Int J Geom Methods Mod Phys, 8:2 (2011), 381–393
Barnich G., Grigoriev M., "First order parent formulation for generic gauge field theories", Journal of High Energy Physics, 2011, no. 1, 122
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
Julve J., Tiemblo A., "A Perturbation Approach to Translational Gravity", Int. J. Geom. Methods Mod. Phys., 10:10 (2013), 1350062
Ivanov E.A., "Gauge fields, nonlinear realizations, supersymmetry", Phys. Part. Nuclei, 47:4 (2016), 508–539
Arbuzov A.B., Cirilo-Lombardo D.J., "Dynamical Symmetries, Coherent States and Nonlinear Realizations: the So(2,4) Case", Int. J. Geom. Methods Mod. Phys., 15:1 (2018), 1850005
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