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.

12 pages, LaTeX, version published on CQG

References in corpus (12)

• Multi-Particle States in Deformed Special Relativity
• Scalar field theory in Snyder space-time: alternatives
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• Snyder space revisited
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
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• 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
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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