Group of boost and rotation transformations with two observer-independent scales

Bruno, N. Rossano

doi:10.1016/s0370-2693(02)02738-7

Cited by 8 publications

(6 citation statements)

References 20 publications

(68 reference statements)

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“…On the contrary, the "position-like" ones (ŷ 3 , ŷ) do not commute; they depend on both ξ and x (see (18)). We stress that this quantum Poincaré group property is in full agreement with the study developed in [71,72] by working with the (dual) quantum algebra. In these works it is shown how the κdeformed Poincaré boost transformations close a group as in the non-deformed case, and the additivity of the boost parameter for transformations along a same direction is also preserved.…”

Section: Non-commutative Spaces Of Worldlinessupporting

confidence: 83%

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

Ballesteros

Bruno

Herranz

2017

Advances in High Energy Physics

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The -deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel' d-double and the Poisson-Lie structure underlying the -deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson-Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the -Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of "duality" between the cosmological constant and the Planck scale is also envisaged.

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Section: Non-commutative Spaces Of Worldlinessupporting

confidence: 83%

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

Ballesteros

Bruno

Herranz

2017

Advances in High Energy Physics

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“…In fact, these results can be seen as different attempts to develop new approaches to physics at the Planck scale, an idea that was early presented in [6]. A further physical development of the κ-Poincaré algebra has led to the so called doubly special relativity (DSR) theories [7,8,9,10,11] that analyse the fundamental role assigned to the deformation parameter/Planck length as an observer-independent length scale to be considered together with the usual observer-independent velocity scale c, in such a manner that Lorentz invariance is preserved [12,13,14].…”

Section: Introductionmentioning

confidence: 99%

A non-commutative Minkowskian spacetime from a quantum AdS algebra

2003

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A quantum deformation of the conformal algebra of the Minkowskian spacetime in $(3+1)$ dimensions is identified with a deformation of the $(4+1)$-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known $\kappa$-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian spacetime is constructed through the full (all orders) dual quantum group spanned by deformed Poincar\'e and dilation symmetries. Although Lorentz invariance is lost, the resulting non-commutative spacetime is quantum group covariant, preserves space isotropy and, furthermore, can be interpreted as a generalization of the $\kappa$-Minkowski space in which a variable fundamental scale (Planck length) appears.Comment: Revised version accepted for pubblication on PLB. Latex file, 9 page

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“…As a straightforward consequence, if both deformed boost transformations are performed along the same direction u 1 = u 2 , then θ = 0 and n = 0, so that P ′ µ = P ′ µ (ξ 1 + ξ 2 ; P 0 µ ), and thus we obtain the additivity of the rapidity in the same way as for κ-Poincaré [33].…”

Section: Deformed Finite Boost Transformationsmentioning

confidence: 74%

“…The explicit form of the commutation rules [K i , P µ ] in (2.1) show that the action of the boost generators on momentum space is deformed, so we can expect that the associated finite boost transformations are also deformed similarly to the κ-Poincaré case [11,18,33].…”

Section: Deformed Finite Boost Transformationsmentioning

confidence: 99%

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

Ballesteros

Bruno

Herranz

2003

J. Phys. A: Math. Gen.

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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.

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Group of boost and rotation transformations with two observer-independent scales

Cited by 8 publications

References 20 publications

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

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

A non-commutative Minkowskian spacetime from a quantum AdS algebra

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

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