Classical dynamics on curved Snyder space

Abstract

We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parametrizing the solutions in terms of an auxiliary time variable, which is a function only of the physical time and of the energy and angular momentum of the particles, one can reduce the problem to the equivalent one in classical mechanics. We also discuss a relativistic extension of these results, and a generalization to the case in which the algebra is realized in flat space.

arXiv comment12 pages, LaTeX, version published on CQG

References in corpus (30)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Non-commutative space-time of Doubly Special Relativity theories
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Triply Special Relativity
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• Multi-Particle States in Deformed Special Relativity
• The Kepler problem and non commutativity
• Snyder noncommutative space-time from two-time physics
• Scalar field theory in Snyder space-time: alternatives
• Snyder space revisited
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Linear Form of 3-scale Relativity Algebra and the Relevance of Stability
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Doubly special relativity in de Sitter spacetime
• Particle Dynamics on Snyder space
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Doubly special relativity and translation invariance
• The Area Quantum and Snyder Space
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• The Kepler problem in the Snyder space
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Snyder-de Sitter model from two-time physics
• The Atick-Witten free energy, closed tachyon condensation and deformed Poincare' symmetry

Cited by in corpus (22)

• Parameters of noncommutativity in Lie-algebraic noncommutative space
• Snyder dynamics in a Schwarzschild spacetime
• Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures
• The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• Generalizations of Snyder model to curved spaces
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation
• Noncommutative Yang model and its generalizations
• Macroscopic body in Snyder space and minimal length estimation
• Graphene in curved Snyder space
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• Noncommutative spaces and covariant formulation of statistical mechanics
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• Black hole thermodynamics in Snyder phase space
• Two-particle system in Coulomb potential for twist-deformed space-time
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Three dimensional DKP oscillator in a curved Snyder space
• Snyder and their representation with creation and annihilation operators
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism