Introduction to Doubly Special Relativity

TL;DR

The paper addresses how Lorentz symmetry can survive at Planck-scale while a second observer-independent scale $\kappa$ is present. It develops the Doubly Special Relativity framework using the $\kappa$-Poincaré Hopf algebra and $\kappa$-Minkowski spacetime, with a de Sitter momentum space representing curved energy-momentum space. It provides explicit one-particle realizations (DSR1/DSR2), a deformed dispersion relation (Casimir), and an analysis of velocity definitions and co-products affecting multi-particle kinematics. The work shows how quantum gravity hints relate to DSR and outlines key open problems, including multi-particle conservation laws and spectator effects, with potential experimental tests through time-of-flight measurements.

Abstract

In these notes, based on the lectures given at 40th Winter School on Theoretical Physics, I review some aspects of Doubly Special Relativity (DSR). In particular, I discuss relation between DSR and quantum gravity, the formal structure of DSR proposal based on $κ$-Poincaré algebra and non-commutative $κ$-Minkowski space-time, as well us some results and puzzles related to DSR phenomenology.