5-Dimensional $SO(1, 4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal

TL;DR

This paper derives the Magueijo-Smolin Doubly Special Relativity from a 5D invariant action, revealing how a deformed dispersion relation and invariant scale emerge naturally through gauge fixing and geometric interpretation.

Contribution

It introduces a 5D $SO(1,4)$-invariant action framework that reproduces the Doubly Special Relativity proposal with a clear geometric and gauge-theoretic foundation.

Findings

Deformed dispersion relation arises as a gauge choice.

Invariant scale appears as a coupling constant.

Geometric interpretation links gauge fixing to relativistic particle dynamics.

Abstract

In this paper we discuss how the Magueijo-Smolin Doubly Special Relativity proposal may obtained from a singular Lagrangian action. The deformed energy-momentum dispersion relation rises as a particular gauge, whose covariance imposes the non-linear Lorentz group action. Moreover, the additional invariant scale is present from the beginning as a coupling constant to a gauge auxiliary variable. The geometrical meaning of the gauge fixing procedure and its connection to the free relativistic particle are also described.