Curvature from quantum deformations

Abstract

A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of non-constant curvature. Such a curvature depends on the quantum deformation parameter z and the flat case is recovered in the limit z\to 0. A superintegrable geodesic dynamics can also be defined in the same framework, and the corresponding spaces turn out to be either Riemannian or relativistic spacetimes (AdS and dS) with constant curvature equal to z. The underlying coalgebra symmetry of this approach ensures the existence of its generalization to arbitrary dimension.

10 pages, LaTeX

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Cited by in corpus (15)

• Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
• Superintegrability on Three-Dimensional Riemannian and Relativistic Spaces of Constant Curvature
• (Super)integrability from coalgebra symmetry: formalism and applications
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Integrable potentials on spaces with curvature from quantum groups
• N-dimensional sl(2)-coalgebra spaces with non-constant curvature
• On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications
• (Anti)de Sitter/Poincare symmetries and representations from Poincare/Galilei through a classical deformation approach
• Contractions, deformations and curvature
• Superintegrability on sl(2)-coalgebra spaces
• Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature
• Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations
• Non-coboundary Poisson-Lie structures on the book group
• Superintegrable potentials on 3D Riemannian and Lorentzian spaces with non-constant curvature
• Integrable potentials on Cayley-Klein spaces from quantum groups