Velocity of particles in Doubly Special Relativity

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 nontrivial 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.

Lagrangian for doubly special relativity particle and the role of noncommutativity

“…Lastly, m = κ ⇒| v |=| p | /m so that Planck mass particles appear to be non-relativistic, which agrees with their dispersion relation (1). All these conclusions are in accord with [15]. In the two figures (i) and (ii) for m = 1, κ = 1.5 and m = 1, κ = 3 respectively, we plot p 2 ≡ A(x), v 2 ≡ C(x) against energy p 0 ≡ x for the MS particle and compare them with the normal particle p 2 ≡ B(x), v 2 ≡ D(x).…”

Doubly special relativity and de Sitter space

“…However, as shown in [28], these variables have physical interpretation of four velocities. More specifically, if we have a point particle carrying energy/momentum (p 0 , p i ) and if we compute the four-velocity of the particle using the standard hamiltonian method, and taking care of the non-trivial phase space structure of DSR, in any DSR theory we find u µ = η µ .…”

Canonical doubly special relativity theory

“…Whereas (27) gives the maximal speed of signals on the background of a mass m, [16] derives the velocity of point particles on the basis of deformed Poisson brackets of its phase space variables and [17] calculates group velocities of wave packets. Beside these two mentioned examples, [18] gives a brief overview over further different constructions of velocity.…”