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Journal of Mathematical Sciences

, Volume 153, Issue 6, pp 799–827 | Cite as

The possibility of relativistic Finslerian geometry

  • V. I. Noskov
Article

Abstract

Foundations of Finslerian geometry that are of interest for solving the problem of geometrization of classical electrodynamics in metric four-dimensionality are investigated. It is shown that parametrization of the interval—the basic aspect of geometry—is carried out non-relativistically. A relativistic way of parametrization is suggested, and the corresponding variant of the geometry is constructed. The equation for the geodesic of this variant of geometry, aside from the Riemannian, has a generalized Lorentz term, the connection contains an additional Lorentz tensorial summand, and the first schouten is different from zero. Some physical consequences of the new geometry are considered: the non-measurability of the generalized electromagnetic potential in the classical case and its measurability on quantum scales (the Aharonov-Bohm effect); it is shown that in the quantum limit the hypothesis of discreteness of space-time is plausible. The linear effect with respect to the field of the “redshift” is also considered and contemporary experimental possibilities of its registration are estimated; it is shown that the experimental results could uniquely determine the choice between the standard Riemannian and relativistic Finslerian models of space-time.

Keywords

Geodesic Equation Natural Parametrization Torsion Tensor Parallel Translation Finslerian Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of Mechanics of Continuous Media of the Ural Division of the RASMoscowRussia

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