Finsler geometry
2013jlz | Garas’ko G.I.  // Electrotechnical Institute of Russia, Moscow, Russia, gri9z@yandex.ru, gri9z.wordpress.com

If before Finsler geometry pretends only on geometrization of classical mechanics than after formulation of Finsler geometry self-sufficiency principle we can speaking that the geometry pretends on whole physics geometrization. From that principle follow field theory equations and electromagnetic field and gravitational field naturally unified in four-dimensional pseudo-Riemannian space and in curved Berwald-Moore space. Energy momentum tensor concerned with conservation laws follows from E. Neter theorem. In weak fields approach from Finsler geometry self-sufficiency principle follows linear field theory equations for several independent fields. In opposite case field equations becomes nonlinear and fields becomes non-independent that leads to superposition principle nonfulfillment. In any Finsler space exists a field or some fields in that space may be supplemented with field, which make sense of action as function of coordinates and analogous to real part of complex potential on Euclidean plane. We propose name such potential as conformal potential. Nondegenerate polynumbers are finslerian spaces, which are very interesting itself and possibly may use in physics. For any finslerian space is possible to build equation analogous to Schrodinger equation or Klein-Gordon equation. This means that the geometry allows further quantum-mechanical development.

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