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

Physics Letters B, 2021 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.