2+1 gravity and Doubly Special Relativity

TL;DR

This paper demonstrates that 2+1 dimensional gravity coupled with point particles exemplifies Doubly Special Relativity, clarifying its algebraic structure and suggesting implications for high-energy particle kinematics in 3+1 dimensions.

Contribution

It explicitly connects 2+1 gravity with DSR, providing a concrete example and resolving ambiguities in the algebra of observables.

Findings

2+1 gravity coupled to particles models DSR.

Explicit transformation between gravity phase space and DSR algebra.

Implication that high-energy 3+1D kinematics may be described by DSR.

Abstract

It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of Doubly Special Relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a $DSR$ system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.