Five-Dimensional Mechanics as the Starting Point for the Magueijo-Smolin Doubly Special Relativity

TL;DR

This paper derives the kinematical rules of doubly special relativity from a five-dimensional mechanics framework with SO(1,4) symmetry, revealing a geometric origin for the deformed energy-momentum relations.

Contribution

It introduces a novel five-dimensional mechanics approach to derive doubly special relativity kinematics from a singular Lagrangian with SO(1,4) symmetry.

Findings

Deformed energy-momentum relation emerges in a specific gauge.

Nonlinear Lorentz transformations are derived from gauge covariance.

Framework provides geometric insight into doubly special relativity.

Abstract

We discuss a way to obtain the doubly special relativity kinematical rules (the deformed energy-momentum relation and the nonlinear Lorentz transformations of momenta) starting from a singular Lagrangian action of a particle with linearly realized SO(1,4) symmetry group. The deformed energy-momentum relation appears in a special gauge of the model. The nonlinear transformations of momenta arise from the requirement of covariance of the chosen gauge.