5 research outputs found
Velocity of particles in Doubly Special Relativity
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.Comment: 12 page
Doubly Special Relativity and de Sitter space
In this paper we recall the construction of Doubly Special Relativity (DSR)
as a theory with energy-momentum space being the four dimensional de Sitter
space. Then the bases of the DSR theory can be understood as different
coordinate systems on this space. We investigate the emerging geometrical
picture of Doubly Special Relativity by presenting the basis independent
features of DSR that include the non-commutative structure of space-time and
the phase space algebra. Next we investigate the relation between our geometric
formulation and the one based on quantum -deformations of the
Poincar\'e algebra. Finally we re-derive the five-dimensional differential
calculus using the geometric method, and use it to write down the deformed
Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde
A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra
A mass-like quantum Weyl-Poincare algebra is proposed to describe, after the
identification of the deformation parameter with the Planck length, a new
relativistic theory with two observer-independent scales (or DSR theory).
Deformed momentum representation, finite boost transformations, range of
rapidity, energy and momentum, as well as position and velocity operators are
explicitly studied and compared with those of previous DSR theories based on
kappa-Poincare algebra. The main novelties of the DSR theory here presented are
the new features of momentum saturation and a new type of deformed position
operators.Comment: 13 pages, LaTeX; some references and figures added, and terminology
is more precis
New varying speed of light theories
We review recent work on the possibility of a varying speed of light (VSL).
We start by discussing the physical meaning of a varying , dispelling the
myth that the constancy of is a matter of logical consistency. We then
summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz
invariance; bimetric theories (where the speeds of gravity and light are not
the same); locally Lorentz invariant VSL theories; theories exhibiting a color
dependent speed of light; varying induced by extra dimensions (e.g. in the
brane-world scenario); and field theories where VSL results from vacuum
polarization or CPT violation. We show how VSL scenarios may solve the
cosmological problems usually tackled by inflation, and also how they may
produce a scale-invariant spectrum of Gaussian fluctuations, capable of
explaining the WMAP data. We then review the connection between VSL and
theories of quantum gravity, showing how ``doubly special'' relativity has
emerged as a VSL effective model of quantum space-time, with observational
implications for ultra high energy cosmic rays and gamma ray bursts. Some
recent work on the physics of ``black'' holes and other compact objects in VSL
theories is also described, highlighting phenomena associated with spatial (as
opposed to temporal) variations in . Finally we describe the observational
status of the theory. The evidence is currently slim -- redshift dependence in
the atomic fine structure, anomalies with ultra high energy cosmic rays, and
(to a much lesser extent) the acceleration of the universe and the WMAP data.
The constraints (e.g. those arising from nucleosynthesis or geological bounds)
are tight, but not insurmountable. We conclude with the observational
predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio