Kinematics in Finsler space is investigated. It is shown that the result based on the kinematics with a special Finsler structure is in good agreement with the reported value of the secular trend in the astronomical unit, dAU/dt = 15 ±4[m/century]. The space deformation parameter A in this special structure is very small, with a scale of 10^-6, and should be a constant. This is consistent with the reported value of an anomalous secular eccentricity variation of the Moon＇s orbit.
We have developed a path integral formalism of the quantum mechanics in the rotating frame of reference, and proposed a path integral description of spin degrees of freedom, which is connected to the Schwinger bosons realization of the angular momenta. We have also given several important examples for the applications in the rotating frames.
We present an explicit connection between the symmetries in a Very Special Relativity （VSR） and isometric group of a specific Finsler space. It is shown that the line element that is invariant under the VSR symmetric group is a Finslerian one. The Killing vectors in Finsler space are constructed in a systematic way. The Lie algebras corresponding to the symmetries of VSR are obtained from a geometric famework. The dispersion relation and the Lorentz invariance violation effect in the VSR are discussed.
