Velocity of particles in Doubly Special Relativity

TL;DR

This paper explores how particle velocities are defined and behave in Doubly Special Relativity, revealing that massless particles always move at the speed of light and clarifying the relation between boost parameters and velocity.

Contribution

It provides a general expression for four-velocity in DSR and demonstrates that massless particles have velocity equal to 1 across all DSR theories.

Findings

Massless particles have velocity equal to 1 in all DSR theories.

Derived the general expression for four-velocity in DSR.

Clarified the relation between boost parameter and velocity.

Abstract

Doubly Special Relativity (DSR) is a class of theories of relativistic motion with two observer-independent scales. We investigate the velocity of particles in DSR, defining velocity as the Poisson bracket of position with the appropriate hamiltonian, taking care of the non-trivial structure of the DSR phase space. We find the general expression for four-velocity, and we show further that the three-velocity of massless particles equals 1 for all DSR theories. The relation between the boost parameter and velocity is also clarified.