Lorentz Invariance Violation and Symmetry in Randers--Finsler Spaces

TL;DR

This paper explores how Randers--Finsler spaces can model Lorentz Invariance violation, introducing modified symmetries and invariants that could relate to Planck-scale physics.

Contribution

It demonstrates that Randers spaces naturally lead to modified dispersion relations and symmetries, providing a geometric framework for Lorentz Invariance violation beyond standard special relativity.

Findings

Derived modified dispersion relations from Randers spaces.

Identified new invariants, including a potential Planck-scale invariant speed.

Established a group structure for the symmetry transformations.

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.