Fundamental principles of physics and Finsler geometry

Abstract

The present work is devoted to the analysis of Finsler geometry. More exactly there are investigated its possibilities to be a basis for generalized theories of interactions. Finsler geometry is one of the generalizations of Riemannian geometry. In Finslerian geometry, manifolds with a Finsler metric are considered; That is, the choice of the norm on each tangent space that varies smoothly from point to point. Finsler's geometrization of space-time makes it possible to develop the theory of physical fields with various internal symmetries, relying on the notion of the group of transformations of tangent vectors leaving the Finsler invariant metric function. The common properties of Finsler geometry and their reductions to classical cases are discussed. It is shown that Finsler geometry is a natural generalization for geometrical bases of all basic theoretical models like General Relativity, Yang-Mills theory, gauge gravity, Kaluza-Klein theories. On the comparison of the theories the properties of the future relevant grand unification theory are predicted. The meaningful application of Finsler geometry to physics can help to take a fresh look at classical and widely known problems, and also help in building new approaches in problem areas.