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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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English version:
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
\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
\jour Theoret. and Math. Phys.
\yr 1974
\vol 21
\issue 3
\pages 1179--1188

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    This publication is cited in the following articles:
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    2. E. A. Ivanov, “On $\Sigma$ models of spontane ously broken symmetries”, Theoret. and Math. Phys., 28:3 (1976), 814–821  mathnet  crossref  mathscinet
    3. V. N. Pervushin, “Dynamical affine symmetry and covariant perturbation theory for gravitation”, Theoret. and Math. Phys., 27:1 (1976), 302–306  mathnet  crossref  mathscinet  zmath
    4. A. B. Borisov, “Unitary representations of the algebra of the general covariance group”, Theoret. and Math. Phys., 33:3 (1977), 1116–1118  mathnet  crossref  zmath
    5. N. G. Pletnev, “Linear supergravity”, Theoret. and Math. Phys., 43:1 (1980), 313–318  mathnet  crossref  mathscinet  isi
    6. V. P. Akulov, I. A. Bandos, V. G. Zima, “Nonlinear realization of extended superconformal symmetry”, Theoret. and Math. Phys., 56:1 (1983), 635–642  mathnet  crossref  isi
    7. 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  mathnet  crossref  mathscinet  isi
    8. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. Ivanov, EA, “AdS branes from partial breaking of superconformal symmetries”, Physics of Atomic Nuclei, 68:10 (2005), 1713  crossref  isi
    10. Ivanov, E, “Higher spins from non-linear realizations of OSp(1 vertical bar 8)”, Physics Letters B, 624:3–4 (2005), 304  crossref  isi
    11. Tiemblo, A, “Gravitational contribution to fermion masses”, European Physical Journal C, 42:4 (2005), 437  crossref  isi
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    13. Zakharov, AF, “Tetrad formalism and reference frames in general relativity”, Physics of Particles and Nuclei, 37:1 (2006), 104  crossref  isi
    14. Leclerc, M, “The Higgs sector of gravitational gauge theories”, Annals of Physics, 321:3 (2006), 708  crossref  isi
    15. West, P, “E-11 and higher spin theories”, Physics Letters B, 650:2–3 (2007), 197  crossref  mathscinet  adsnasa  isi
    16. 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  crossref  isi
    17. Yang H.S., “Emergent Gravity From Noncommutative Space-Time”, Int. J. Mod. Phys. A, 24:24 (2009), 4473–4517  crossref  isi
    18. 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  crossref  isi
    19. McArthur I.N., “Nonlinear realizations of symmetries and unphysical Goldstone bosons”, Journal of High Energy Physics, 2010, no. 11, 140  isi
    20. Grigoriev M., “Parent formulation at the Lagrangian level”, Journal of High Energy Physics, 2011, no. 7, 061  isi
    21. Julve J., Tiemblo A., “Dynamical Variables in Gauge-Translational Gravity”, Int J Geom Methods Mod Phys, 8:2 (2011), 381–393  crossref  isi
    22. Barnich G., Grigoriev M., “First order parent formulation for generic gauge field theories”, Journal of High Energy Physics, 2011, no. 1, 122  isi
    23. 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  crossref  isi
    24. Julve J., Tiemblo A., “A Perturbation Approach to Translational Gravity”, Int. J. Geom. Methods Mod. Phys., 10:10 (2013), 1350062  crossref  isi
    25. Ivanov E.A., “Gauge fields, nonlinear realizations, supersymmetry”, Phys. Part. Nuclei, 47:4 (2016), 508–539  crossref  isi  elib  scopus
    26. 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  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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