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J. Sib. Fed. Univ. Math. Phys., 2009, Volume 2, Issue 4, Pages 432–448 (Mi jsfu91)  

This article is cited in 9 scientific papers (total in 9 papers)

Connection of Young-Mills Equations with Einstein and Maxwell's Equations

Leonid N. Krivonosov, Vyacheslav A. Luk'yanov

Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia

Abstract: In this article it is shown that Young-Mills equations on a 4-dimensional conformally connected manifold without torsion may be reduced to three groups of equations: 10 Einstein equations, 8 Maxwell's equations and 9 equations of substance movement. In the given work successful unification of gravitation and electromagnetism in the model of conformally connected manifold without torsion is carried out. It makes the idea of unification of all four kinds of interactions in the Nature within the framework of the 4-dimensional conformally connected manifold with torsion optimistic.

Keywords: curvature of the connection, torsion of the connection, Hodge operator, Bianchi identity, Einstein equations, Maxwell's equations, Young-Mills equations, 4-dimensional conformally connected manifold.

Full text: PDF file (227 kB)
References: PDF file   HTML file
UDC: 515.1
Received: 12.06.2009
Received in revised form: 11.11.2009
Accepted: 20.11.2009

Citation: Leonid N. Krivonosov, Vyacheslav A. Luk'yanov, “Connection of Young-Mills Equations with Einstein and Maxwell's Equations”, J. Sib. Fed. Univ. Math. Phys., 2:4 (2009), 432–448

Citation in format AMSBIB
\Bibitem{KriLuk09}
\by Leonid~N.~Krivonosov, Vyacheslav~A.~Luk'yanov
\paper Connection of Young-Mills Equations with Einstein and Maxwell's Equations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2009
\vol 2
\issue 4
\pages 432--448
\mathnet{http://mi.mathnet.ru/jsfu91}


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

    This publication is cited in the following articles:
    1. Leonid N. Krivonosov, Vyacheslav A. Lukyanov, “Polnoe reshenie uravnenii Yanga–Millsa dlya tsentralno-simmetricheskoi metriki”, Zhurn. SFU. Ser. Matem. i fiz., 4:3 (2011), 350–362  mathnet
    2. Leonid N. Krivonosov, Vyacheslav A. Lukyanov, “Uravneniya Einshteina na chetyrekhmernom mnogoobrazii konformnoi svyaznosti bez krucheniya”, Zhurn. SFU. Ser. Matem. i fiz., 5:3 (2012), 393–408  mathnet
    3. Leonid N. Krivonosov, Vyacheslav A. Lukyanov, “Purely time-dependent solutions to the Yang–Mills equations on a $4$-dimensional manifold with conformal torsion-free connection”, Zhurn. SFU. Ser. Matem. i fiz., 6:1 (2013), 40–52  mathnet
    4. Leonid N. Krivonosov, Vyacheslav A. Luk'yanov, Lubov V. Voloskova, “Extremal curves in the conformal space and in an associated bundle”, Zhurn. SFU. Ser. Matem. i fiz., 7:1 (2014), 68–78  mathnet
    5. L. N. Krivonosov, V. A. Lukyanov, “Kalibrovochno-invariantnye tenzory 4-mnogoobraziya konformnoi svyaznosti bez krucheniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(35) (2014), 180–198  mathnet  crossref  zmath  elib
    6. L. N. Krivonosov, V. A. Lukyanov, “Polnoe reshenie uravnenii Yanga–Millsa dlya tsentralno-simmetricheskoi metriki pri nalichii elektromagnitnogo polya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:3 (2015), 462–473  mathnet  crossref  zmath  elib
    7. V. A. Lukyanov, L. N. Krivonosov, “Uravneniya Yanga-Millsa na 4-mnogoobraziyakh konformnoi svyaznosti bez krucheniya s razlichnymi signaturami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:4 (2017), 633–650  mathnet  crossref  zmath  elib
    8. L. N. Krivonosov, V. A. Luk'yanov, “The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space”, J. Math. Sci., 231:2 (2018), 189–205  mathnet  crossref  crossref
    9. L. N. Krivonosov, V. A. Lukyanov, “Osnovnaya teorema dlya (anti)avtodualnoi konformnoi svyaznosti bez krucheniya na chetyrekhmernom mnogoobrazii”, Izv. vuzov. Matem., 2019, no. 2, 29–38  mathnet  crossref
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