Extended Non Linear Conformal Symmetry and DSR Velocities on the Physical Surface

TL;DR

This paper explores the extension of conformal symmetry and its relation to Deformed Special Relativity velocities, demonstrating isomorphisms between different spacetime models and solving position space dynamics.

Contribution

It introduces an extended nonlinear conformal algebra and establishes isomorphisms between massless particles in various spacetime dimensions, linking conformal symmetry with DSR velocities.

Findings

Extended conformal algebra with nonlinear structure

Isomorphism between massless particles in different spacetime models

Explicit solution to position space dynamics

Abstract

The relation between Conformal generators and Magueijo Smolin Deformed Special Relativity term, added to Lorentz boosts, is achieved. The same is performed for Fock Lorentz transformations. Through a dimensional reduction procedure, it is demonstrated that a massless relativistic particle living in a $d$ dimensional space, is isomorphic to one living in a $d+2$ space with pure Lorentz invariance and to a particle living in a $AdS_{d+1}$ space. To accomplish these identifications, the Conformal Group is extended and a nonlinear algebra arises. Finally, because the relation between momenta and velocities is known, the problem of position space dynamics is solved.