Doubly Special Relativity with light-cone deformation

TL;DR

This paper introduces a novel Doubly Special Relativity framework based on light-cone deformation of the $ppa$-Poincare9 algebra, leading to non-commutative spacetime and modified Lorentz symmetries.

Contribution

It generalizes the $ppa$-deformation to null directions, deriving phase space relations and analyzing the impact on Lorentz symmetry and spacetime structure.

Findings

Space-time becomes non-commutative under the new deformation.

The Lorentz algebra splits into kinematical and dynamical parts.

Emergence of two-dimensional Galilean symmetry in the null basis.

Abstract

We propose a new Doubly Special Relativity theory based on the generalization of the $\kappa$-deformation of the Poincar\'e algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincar\'e algebra and use it to derive the phase space commutation relations. As in the DSR based on the standard quantum $\kappa$-Poincar\'e algebra we find that the space time is non-commutative. We investigate the fate of the properties of Special Relativity in the null basis: the split of the algebra of Lorentz and momentum generators into kinematical and dynamical parts, the action of the kinematical boost $M^{+-}$, and the emergence of the two dimensional Galilean symmetry.