A new  doubly special relativity  theory from a quantum Weyl–Poincaré algebra

Abstract

A 'mass-like' quantum Weyl-Poincaré 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 κ-Poincaré 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.

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

“…These deformed Poincaré symmetries were later applied in the context of the so-called doubly special relativity (DSR) theories [24][25][26][27][28][29][30][31][32] which introduced two fundamental scales: the usual observer-independent velocity scale as well as an observer-independent length scale , which was related to the deformation parameter in the algebra. Since from all approaches to quantum gravity [33][34][35][36][37] the Planck scale is thought to play a fundamental role, DSR theories seem to establish a promising link between some Planck scale effects and quantum groups [38,39].…”

Doubly-Special Relativity: Facts, Myths and Some Key Open Issues

“…As in the case of the κ-Poincaré/κ-Minkowski framework, the idea that this framework based on canonical noncommutativity might provide the basis for a DSR theory originates essentially in the observation that the spacetime noncommutativity of canonical form, (22), is left invariant by the action of the Hopf-algebra generators (23)- (24), so that any physical consequence of that noncommutativity (such as "spacetime fuzzyness") should be observer independent. To render explicit the presence of a short invariant length scale one can conveniently rewrite the observer-independent dimensionful matrix θ µν in terms of an observer-independent length scale λ and an observer-independent dimensionless matrix τ µν (with an extra restriction, e.g., unit determinant, to avoid apparent overcounting of parameters upon introducing λ): θ µν = λ 2 τ µν .…”

Conformal Group With Two Observer Independent Scales

“…It has been also recently conjectured that the κ-Poincaré algebra may provide the basis for a so-called doubly special relativity (DSR) 4,5,6,7 in which the deformation parameter/Planck length is viewed as an observer-independent length scale completely analogous to the familiar observer-independent velocity scale c, in such a manner that (deformed) Lorentz invariance is preserved 8,9,10 . In this talk I want to review briefly some related results which have been presented in greater detail in [11,12]. These results provide an analysis of the Poincaré sector of a manageable deformation of so(4, 2) introduced in [13] together with its dual in order to extract some physical implications on the associated non-commutative Minkowskian spacetime.If {J i , P µ = (P 0 , P), K i , D} denote the generators of rotations, time and space translations, boosts and dilations, the non-vanishing deformed commutation rules 1…”