Lorentz invariance violation and symmetry in Randers–Finsler spaces

Zhe Chang,Xin Li

doi:10.1016/j.physletb.2008.03.045

Abstract

Lorentz invariance violation is a common feature of new physics beyond the Standard Model. We show that the symmetry of Randers spaces deduces a modified dispersion relation with characteristics of Lorentz invariance violation. The counterparts of the Lorentz transformation in the Einstein's special relativity are presented explicitly. The coordinate transformations are unitary and form a group. Generators and algebra satisfied by them are different from usual Lorentz ones. The Randersian line element as well as speed of light is invariant under the transformations. In particular, there is another invariant speed which may be related with Planck scale and the mass of moving particle. Thus, the Randers spaces is a suitable framework to discuss the Lorentz invariance violation.

Highlights

Lorentz Invariance violation is a common feature of new physics beyond the standard model
The theory with SIM(2) symmetry is refereed as the Very Special Relativity (VSR)
Liberati and Sindoni[15] showed that the modified dispersion relations (MDR) can be incorporated into the framework of Finsler geometry

Summary

Finsler geometry has its genesis in integrals of the form r

S dτ dτ Throughout the Letter, the lowering and raising of indices are carried out by the fundamental tensor gij defined above, and its matrix inverse gij.

Define the canonical momentum pi as pi

Both Λij and mations form

Jij xi P j xj Pi and