De Sitter space as an arena for Doubly Special Relativity

TL;DR

This paper presents a geometric interpretation of Doubly Special Relativity by modeling energy-momentum space as de Sitter space, unifying various formulations and addressing key conceptual issues.

Contribution

It introduces a geometric framework for DSR using de Sitter space, clarifying the universality of non-commutative space-time and proposing natural bases for the theory.

Findings

Different DSR bases correspond to different coordinate systems on de Sitter space

The geometric picture explains the universality of non-commutative space-time structure

Provides insights into the total momentum problem in multi-particle systems

Abstract

We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy-momentum space being the four dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as different coordinate systems on this space. The emerging geometrical picture makes it possible to understand the universality of the non-commutative structure of space-time of Doubly Special Relativity. Moreover, it suggests how to construct the most natural DSR bases and makes it possible to address the long standing problem of total momentum of many particle systems from a different perspective.