Problems of Finslerian theory of gauge fields and gravitation (Q1825452)

The main purpose of the present paper is to give a systematic analysis of post-Newtonian techniques for a Finsler extension of the gravity theory related to its observational consequences. First, there are studied the orbital gravitational effects in case of special representations of a Finslerian anisotropic post-Newtonian metric. Then there are obtained generalizations of both the geodesics equations and the Maxwell equations. Further, there are investigated two generalized Finsler metrics, the Finsler connections associated with them and it is calculated the gyroscope precession effect for these metrics. Finally, there are introduced and studied Finsler gauge fields, Finsler gauge covariant derivatives and Lie derivatives of Finsler gauge fields. It seems to the reviewer that Finsler geometry should be considered by now as the mathematical background of multi-dimensional physical theories. Certainly, the paper under review supports our assertion.