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TMF, 2011, Volume 166, Number 3, Pages 323–335 (Mi tmf6614)  

This article is cited in 21 scientific papers (total in 21 papers)

New dynamical variables in Einstein's theory of gravity

L. D. Faddeev

St.~Petersburg Branch of the~Steklov Institute of Mathematics, RAS, St.~Petersburg, Russia

Abstract: We describe an alternative formalism for Einstein's theory of gravity. The role of dynamical variables is played by a collection of ten vector fields $f_{\mu}^A$, $A=1,…,10$. The metric is a composite variable, $g_{\mu\nu}=f_{\mu}^Af_{\nu}^A$. The proposed scheme may lead to further progress in a theory of gravity where Einstein's theory is to play the role of an effective theory, with Newton's constant appearing by introducing an anomalous Green's function.

Keywords: Einstein theory of gravity, vector fields, Hamiltonian formulation

DOI: https://doi.org/10.4213/tmf6614

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English version:
Theoretical and Mathematical Physics, 2011, 166:3, 279–290

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Received: 06.09.2010

Citation: L. D. Faddeev, “New dynamical variables in Einstein's theory of gravity”, TMF, 166:3 (2011), 323–335; Theoret. and Math. Phys., 166:3 (2011), 279–290

Citation in format AMSBIB
\by L.~D.~Faddeev
\paper New dynamical variables in Einstein's theory of gravity
\jour TMF
\yr 2011
\vol 166
\issue 3
\pages 323--335
\jour Theoret. and Math. Phys.
\yr 2011
\vol 166
\issue 3
\pages 279--290

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    This publication is cited in the following articles:
    1. Mielke E.W., “Weak equivalence principle from a spontaneously broken gauge theory of gravity”, Phys. Lett. B, 702:4 (2011), 187–190  crossref  mathscinet  adsnasa  isi  elib  scopus
    2. T. A. Bolokhov, “Algebraic properties of the Einstein–Cartan action”, J. Math. Sci. (N. Y.), 192:1 (2013), 31–36  mathnet  crossref  mathscinet
    3. Paston S.A., Sheykin A.A., “From the embedding theory to general relativity in a result of inflation”, Internat. J. Modern Phys. D, 21:5 (2012), 1250043, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Khatsymovsky V.M., “First-Order Representation of the Faddeev Formulation of Gravity”, Class. Quantum Gravity, 30:9 (2013), 095006  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Mielke E.W., “Symmetry Breaking in Topological Quantum Gravity”, Int. J. Mod. Phys. D, 22:5 (2013), 1330009  crossref  zmath  adsnasa  isi  elib  scopus
    6. Bekenstein J.D., “Can Quantum Gravity Be Exposed in the Laboratory?”, Found. Phys., 44:5 (2014), 452–462  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Sheykin A.A., Paston S.A., “The Approach To Gravity as a Theory of Embedded Surface”, II Russian-Spanish Congress on Particle and Nuclear Physics At All Scales, Astroparticle Physics and Cosmology, AIP Conference Proceedings, 1606, eds. Andrianov A., Espriu D., Andrianov V., Kolevatov S., Amer Inst Physics, 2014, 400–406  crossref  isi  scopus
    8. Khatsymovsky V.M., “First-Order Minisuperspace Model For the Faddeev Formulation of Gravity”, Mod. Phys. Lett. A, 30:32 (2015), 1550174  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. S. A. Paston, “Relation between quantum effects in general relativity and embedding theory”, Theoret. and Math. Phys., 185:1 (2015), 1502–1515  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. A. A. Sheikin, S. A. Paston, “Classification of minimum global embeddings for nonrotating black holes”, Theoret. and Math. Phys., 185:1 (2015), 1547–1556  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. Khatsymovsky V.M., “Spectrum of area in the Faddeev formulation of gravity”, Mod. Phys. Lett. A, 31:19 (2016), 1650114  crossref  mathscinet  zmath  isi  elib  scopus
    12. Paston S.A., Semenova E.N., Franke V.A., Sheykin A.A., “Algebra of implicitly defined constraints for gravity as the general form of embedding theory”, Gravit. Cosmol., 23:1 (2017), 1–7  crossref  mathscinet  zmath  isi  scopus
    13. Mielke E.W., “Color Geometrodynamics”: Mielke, EW, Geometrodynamics of Gauge Fields: on the Geometry of Yang-Mills and Gravitational Gauge Theories, 2Nd Edition, Mathematical Physics Studies, Springer International Publishing Ag, 2017, 329–345  crossref  mathscinet  isi
    14. Khatsymovsky V.M., “First-Order Discrete Faddeev Gravity At Strongly Varying Fields”, Mod. Phys. Lett. A, 32:35 (2017), 1750181  crossref  mathscinet  zmath  isi  scopus
    15. Grad D.A., Ilin R.V., Paston S.A., Sheykin A.A., “Gravitational Energy in the Framework of Embedding and Splitting Theories”, Int. J. Mod. Phys. D, 27:2 (2018), 1750188  crossref  mathscinet  isi  scopus
    16. Paston S.A., Sheykin A.A., “Embedding Theory as New Geometrical Mimetic Gravity”, Eur. Phys. J. C, 78:12 (2018), 989  crossref  isi  scopus
    17. Sheykin A., Solovyev D., Paston S., “Global Embeddings of Btz and Schwarzschild-Ads Type Black Holes in a Flat Space”, Symmetry-Basel, 11:7 (2019), 841  crossref  isi
    18. Ilin R., Paston S., “Energy-Momentum Pseudotensor and Superpotential For Generally Covariant Theories of Gravity of General Form”, Universe, 6:10 (2020), 173  crossref  isi
    19. Paston S., “Non-Relativistic Limit of Embedding Gravity as General Relativity With Dark Matter”, Universe, 6:10 (2020), 163  crossref  isi
    20. Kapustin A.D., Ioffe V M., Paston S.A., “Explicit Isometric Embeddings of Collapsing Dust Ball”, Class. Quantum Gravity, 37:7 (2020), 075019  crossref  mathscinet  isi
    21. Paston S., Semenova E., Sheykin A., “Canonical Description For Formulation of Embedding Gravity as a Field Theory in a Flat Spacetime”, Symmetry-Basel, 12:5 (2020)  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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