Doubly Special Relativity with light-cone deformation

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.