Newton's Second Law in a Noncommutative Space

Abstract

In this work we show that corrections to the Newton's second law appears if we assume that the phase space has a symplectic structure consistent with the rules of commutation of noncommutative quantum mechanis. In the central field case we find that the correction term breaks the rotational symmetry. In particular, for the Kepler problem, this term takes the form of a Coriolis force produced by the weak gravitational field far from a rotating massive object.

7 pages, References added

References in corpus (11)

• String Theory and Noncommutative Geometry
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Noncommutative Field Theory and Lorentz Violation
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Quantum mechanics on the noncommutative plane and sphere
• The Standard Model on Non-Commutative Space-Time
• Two phases of the noncommutative quantum mechanics
• Poincare covariant mechanics on noncommutative space
• A Gravitomagnetic Effect on the Orbit of a Test Body due to the Earth's Variable Angular Momentum
• Noncommutative geometry and the classical orbits of particles in a central force potential

Cited by in corpus (35)

• Spin Hall effect and Berry phase of spinning particles
• Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
• Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
• Bianchi spacetimes in noncommutative phase-space
• Late time acceleration in a deformed phase space model of dilaton cosmology
• Exotic galilean symmetry and non-commutative mechanics
• Newton's Equation on the kappa space-time and the Kepler problem
• Doubly Special Relativity in Position Space Starting from the Conformal Group
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Spacetime singularity resolution in Snyder noncommutative space
• Natural Cutoffs via Compact Symplectic Manifolds
• Classical mechanics of many particles defined on canonically deformed nonrelativistic space-time
• Noncommutative quantum mechanics and Bohm's ontological interpretation
• Noncommutativity in quantum cosmology and the Hierarchy problem
• Noncommutative Geometry and Fluid Dynamics
• Group theoretical construction of planar Noncommutative Phase Spaces
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
• Analytical and numerical analysis of a rotational invariant D=2 harmonic oscillator in the light of different noncommutative phase-space configurations
• Noncommutative Phase Spaces by Coadjoint Orbits Method
• Cosmological Constant and Noncommutativity: A Newtonian point of view
• Noncommutative Brownian motion
• Noncommutative Lagrange Mechanics
• Bohr-van Leeuwen theorem in non-commutative space
• The Henon-Heiles system defined on Lie-algebraically deformed Galilei space-time
• Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space
• Para-Galilean versus Galilean Noncommutative Phase spaces
• Duality between the coordinates and wave functions on noncommutative space
• (2 +1)-dimensional Duffin-Kemmer-Petiau oscillator under a magnetic field in the presence of a minimal length in the noncommutative space
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Perturbed nonlinear models from Noncommutativity
• Equivalent forces in Newton equation from twist deformations and noninertial coordinate frames
• Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism
• Twist deformation of doubly enlarged Newton-Hooke Hopf algebra