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Zbl 0842.53020
Văcaru, Sergiu I.; Goncharenko, Yurii
Yang-Mills fields and gauge gravity on generalized Lagrange and Finsler spaces. (English)
[J] Int. J. Theor. Phys. 34, No.9, 1955-1980 (1995). ISSN 0020-7748; ISSN 1572-9575/e

In the framework of the theory of linear connections in vector bundles (with semisimple structural groups) on generalized Lagrange spaces, a geometrical approach to interactions of Yang-Mills fields on spaces with local anisotropy is formulated. The geometrical formalism is extended in a manner including theories with nonsemisimple groups which permit a unique fiber bundle treatment for both locally anisotropic Yang-Mills and gravitational interactions.\par One of the most important results of the paper is formulated as a theorem stating that almost Hermitian Lagrange gravity -- described in {\it R. Miron} and {\it M. Anastasiei} [The geometry of Lagrange spaces: theory and applications. Fundamental Theories of Physics, 59, Dordrecht: Kluwer Academic Publishers (1994; Zbl 0831.53001)], is equivalent to a gaugelike theory in the bundle of affine adapted frames on generalized Lagrange spaces.
[V.Balan (Bucureşti)]

MSC 2000:: *53C07 Special connections and metrics on vector bundles
81T13 Gauge theories
83C47 Quantum field theory on curved space-times
53Z05 Appl. of differential geometry to physics

Keywords: Finsler spaces; generalized Lagrange geometry; Yang-Mills equations

Citations: Zbl 0831.53001

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