The Kepler problem and non commutativity

Abstract

We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58}{\text{m}}^2$ gives observable corrections to the movement of the solar system. In this way, modifications in the physics of smaller scales implies modifications at large scales, something similar to the UV/IR mixing.

10 pages

References in corpus (4)

• Noncommutative Field Theory and Lorentz Violation
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Testing Non-commutative QED, Constructing Non-commutative MHD
• Superluminal Noncommutative Photons

Cited by in corpus (44)

• Noncommutative Gravity
• Composite system in noncommutative space and the equivalence principle
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• Quantum gravity, minimum length and Keplerian orbits
• Newton's Equation on the kappa space-time and the Kepler problem
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Noncommutative Quantum Cosmology
• On Noncommutative Classical Mechanics
• Classical dynamics on curved Snyder space
• Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle
• Classical mechanics of many particles defined on canonically deformed nonrelativistic space-time
• The Kepler problem in the Snyder space
• Geodesic equation in non-commutative gauge theory of gravity
• Non-singular Brans-Dicke collapse in deformed phase space
• Chiral Bosons in Noncommutative Spacetime
• Non-commutative oscillator with Kepler-type dynamical symmetry
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• On deformations of classical mechanics due to Planck-scale physics
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Orbits of particles in noncommutative Schwarzschild spacetime
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Non-commutative mechanics and Exotic Galilean symmetry
• Two-particle system in noncommutative space with preserved rotational symmetry
• A Review of Noncommutative Field Theories
• Closedness of orbits in a space with SU(2) Poisson structure
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• On Non-commutative Geodesic Motion
• Cosmological Constant and Noncommutativity: A Newtonian point of view
• Noncommutative Brownian motion
• Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle
• Two-particle system in Coulomb potential for twist-deformed space-time
• Central force problem in space with SU(2) Poisson structure
• On Planetary Orbits in Entropic Gravity
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole
• Lyapunov exponents and geodesic stability of Schwarzschild black hole in the non-commutative gauge theory of gravity
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Equivalent forces in Newton equation from twist deformations and noninertial coordinate frames
• Perturbed nonlinear models from Noncommutativity
• Snyder Like Modified Gravity in Newton's Spacetime