Related papers: Lorentz-covariant deformed algebra with minimal le…
The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. For D=3, it includes Snyder algebra as a special…
In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen. {\bf 39}, 10909, 2006) introduced a (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian…
The (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk [C. Quesne and V. M. Tkachuk, J. Phys. A: Math. Gen. \textbf {39}, 10909 (2006).], leads to a nonzero minimal…
In a series of papers, Kempf and co-workers (J. Phys. A: Math. Gen. {\bf 30}, 2093, (1997); Phys. Rev. D {\bf52}, 1108, (1995); Phys. Rev. D {\bf55}, 7909, (1997)) introduced a D-dimensional $(\beta,\beta')$-two-parameter deformed…
Quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions are revisited, and several features of these quantum structures are reviewed. In particular, the classification problem of (2+1) (A)dS Lie bialgebras is presented and the…
This paper introduces a systematic algorithm for deriving a new unitary representation of the Lorentz algebra ($so(1,3)$) and an irreducible unitary representation of the extended (anti) de-Sitter algebra ($so(2,4)$) on…
The Poincar\'e sector of a recently deformed conformal algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, the symmetries of a new relativistic theory with two observer-independent…
We consider $\kappa$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincar\'e algebra is unaltered,…
In the 1990s, Kempf and his collaborators Mangano and Mann introduced a $D$-dimensional $(\beta,\beta')$-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length $(\triangle…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e 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.…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
We construct the full quantum algebra, the corresponding Poisson-Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS)…
We consider the deformation of the Poincar\'e group in 2+1 dimensions into the quantum double of the Lorentz group and construct Lorentz-covariant momentum-space formulations of the irreducible representations describing massive particles…
Unified graded differential algebra, generated by $\kappa$-Minkowski noncommutative (NC) coordinates, Lorentz generators and anticommuting one-forms, is constructed. It is compatible with $\kappa$-Poincar\'e-Hopf algebra. For time- and…
It is argued that the familiar algebra of the non-commutative space-time with $c$-number $\theta^{\mu\nu}$ is inconsistent from a theoretical point of view. Consistent algebras are obtained by promoting $\theta^{\mu\nu}$ to an…
We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional…
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…
We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale \ell_p, and thus breaks scale invariance, but preserves all space-time isometries. The…