Doubly Special Relativity and de Sitter space

TL;DR

This paper explores Doubly Special Relativity as a geometric theory with energy-momentum space modeled as de Sitter space, highlighting basis-independent features, non-commutative geometry, and quantum deformations.

Contribution

It provides a geometric formulation of DSR, connecting it with quantum deformations and deriving a differential calculus for deformed field equations.

Findings

Basis-independent features of DSR identified

Relation between geometric DSR and quantum κ-deformations established

Deformed Klein-Gordon equation derived and analyzed

Abstract

In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.