Quantum (anti)de Sitter algebras and generalizations of the kappa–Minkowski space
نویسندگان
چکیده
We present two different quantum deformations for the (anti)de Sitter algebras and groups. The former is a non-standard (triangular) deformation of SO(4, 2) realized as the conformal group of the (3+1)D Minkowskian spacetime, while the latter is a standard (quasitriangular) deformation of both SO(2, 2) and SO(3, 1) expressed as the kinematical groups of the (2+1)D anti-de Sitter and de Sitter spacetimes, respectively. The Hopf structure of the quantum algebra and a study of the dual quantum group are presented for each deformation. These results enable us to propose new non-commutative spacetimes that can be interpreted as generalizations of the κ– Minkowski space, either by considering a variable deformation parameter (depending on the boost coordinates) in the conformal deformation, or by introducing an explicit curvature/cosmological constant in the kinematical one; κ–Minkowski turns out to be the common first–order structure for all of these quantum spaces. Some properties provided by these deformations, such as dimensions of the deformation parameter (related with the Planck length), space isotropy, deformed boost transformations, etc., are also commented. Communication presented in the XI International Conference on Symmetry Methods in Physics, June 21-24, 2004, Prague, Czech Republic. Electronically published in “Symmetry methods in Physics”, edited by C. Burdik, O. Navrátil and S. Posta, Joint Institute for Nuclear Research, Dubna (Russia), pp. 1-20, (2004).
منابع مشابه
Super algebra and Harmonic Oscillator in Anti de Sitter space
The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...
متن کاملSpacelike hypersurfaces with constant $S$ or $K$ in de Sitter space or anti-de Sitter space
Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and oriented spacelike hypersurface in a de Sitter space or an anti-de Sitter space, $S$ and $K$ be the squared norm of the second fundamental form and Gauss-Kronecker curvature of $M^n$. If $S$ or $K$ is constant, nonzero and $M^n$ has two distinct principal curvatures one of which is simple, we obtain some charact...
متن کاملNon-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti)de Sitter groups
The κ-deformation of the 2+1 anti-de Sitter, Poincaré and de Sitter groups is studied within a unified approach by considering explicitly the curvature of the spacetime (cosmological constant) as a parameter. The Drinfel’d-double construction as well as the Poisson–Lie structure underlying the κ-deformation are explicitly given, and the three quantum groups are obtained as Weyl quantizations of...
متن کاملRepresentations of Classical Lie Algebras from their Quantum Deformations
We make use of a well-know deformation of the Poincaré Lie algebra in dimensions ( ) to construct the Poincaré Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the Poincaré Lie algebra appearing as certain irrational functions of the generators of the de Sitter groups. We have obtained generalizations of this “anti-deformation” for the and cases ...
متن کامل