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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
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\by A.~B.~Borisov, V.~I.~Ogievetskii
\paper Theory of dynamical affine and conformal symmetries as the theory of the gravitational field
\jour TMF
\yr 1974
\vol 21
\issue 3
\pages 329--342
\mathnet{http://mi.mathnet.ru/tmf3902}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=475579}
\transl
\jour Theoret. and Math. Phys.
\yr 1974
\vol 21
\issue 3
\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
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A. B. Borisov, “Unitary representations of the algebra of the general covariance group”, Theoret. and Math. Phys., 33:3 (1977), 1116–1118
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V. P. Akulov, I. A. Bandos, V. G. Zima, “Nonlinear realization of extended superconformal symmetry”, Theoret. and Math. Phys., 56:1 (1983), 635–642
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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
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Julve J., Tiemblo A., “A Perturbation Approach to Translational Gravity”, Int. J. Geom. Methods Mod. Phys., 10:10 (2013), 1350062
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Ivanov E.A., “Gauge fields, nonlinear realizations, supersymmetry”, Phys. Part. Nuclei, 47:4 (2016), 508–539
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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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