Geodesic
Connection of Young-Mills Equations with Einstein and Maxwell's Equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 4, pp. 432-448

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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. 
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     author = {Leonid N. Krivonosov and Vyacheslav A. Luk'yanov},
     title = {Connection of {Young-Mills} {Equations} with {Einstein} and {Maxwell's} {Equations}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Leonid N. Krivonosov; Vyacheslav A. Luk'yanov. Connection of Young-Mills Equations with Einstein and Maxwell's Equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 4, pp. 432-448. http://geodesic.mathdoc.fr/item/JSFU_2009_2_4_a5/