Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann equation and a new luminosity distance-redshift relation is proposed. A best-fit to the Type Ia supernovae （SNe） observations yields that the Λ in the Λ-CDM model is suppressed to almost zero. This fact indicates that the astronomical observations on the Type Ia SNe can be described well without invoking any form of dark energy. The best-fit age of the universe is given. It is in agreement with the age of our galaxy.
With the Coulomb gauge, the Chern-Simons-Georgi-Glashow （CSGG） model is quantized in the Dirac formalism for the constrained system. Combining the Gauss law and Coulomb gauge consistency condition, the difference between the Schwinger angular momentum and canonical angular momentum of the system is found to be an anomalous spin. The reason for this result lies in the fact that the Schwinger energy momentum tensor and the canonical one have different symmetry properties in the presence of the Chern-Simons term.
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 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.
Kinematics in Finsler space is used to study the propagation of ultra high energy cosmic rays particles through the cosmic microwave background radiation. We find that the GZK threshold is lifted dramatically in Randers-Finsler space. A tiny deformation of spacetime from Minkowskian to Finslerian allows more ultra-high energy cosmic rays particles to arrive at the earth. It is suggested that the lower bound of particle mass is related with the negative second invariant speed in Randers-Finsler space.
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.
