Planck-Scale Phenomenology and Symmetry in Randers–Finsler Spaces

Lorentz Violation is a common feature of Planck-scale phenomenology. We show that the symmetry of Randers spaces deduces a modified dispersion relation, which takes the quantum gravity effects into account. 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 is related with Planck scale and the mass of moving particle. This is the feature of Planck scale phenomenology. Thus, the Randers spaces is a suitable framework to discuss the Planck scale effects. PACS numbers: 03.30.+p, 04.60.-m, 11.30.Cp [email protected] [email protected]