Classical mechanics of many particles defined on canonically deformed nonrelativistic space-time

Abstract

We provide the classical mechanics of many particles moving in canonically twist-deformed space-time. In particular, we consider two examples of such noncommutative systems - the set of N particles moving in gravitational field as well as the system of N interacting harmonic oscillators.

15 pages, no figures

References in corpus (29)

• Quantum Field Theory on Noncommutative Spaces
• High-Energy Tests of Lorentz Invariance
• Testable scenario for Relativity with minimum-length
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• New Tests of Lorentz Invariance Following from Observations of the Highest Energy Cosmic Gamma Rays
• An infrared background--TeV gamma-ray crisis?
• Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light
• Comments on the Hydrogen Atom Spectrum in the Noncommutative Space
• Poisson structures on the Poincare group
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Quantum-Gravity Phenomenology: Status and Prospects
• On noncommutative isotropic harmonic oscillator
• Cosmic rays and TeV photons as probes of quantum properties of space-time
• The Kepler problem and non commutativity
• Newton's Second Law in a Noncommutative Space
• Twisted Classical Poincaré Algebras
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Canonical and Lie-algebraic twist deformations of Galilei algebra
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• Oscillator model on Lie-algebraically deformed nonrelativistic space-time

Cited by in corpus (19)

• Composite system in noncommutative space and the equivalence principle
• Composite system in rotationally invariant noncommutative phase space
• Parameters of noncommutativity in Lie-algebraic noncommutative space
• Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle
• Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Noncommutative Geometry and Fluid Dynamics
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Two-particle system in noncommutative space with preserved rotational symmetry
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Features of free particles system motion in noncommutative phase space
• Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin
• Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle
• Non-Grassmann mechanical model of the Dirac equation
• Two-particle system in Coulomb potential for twist-deformed space-time
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• Features of description of composite system's motion in twist-deformed space-time