Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space

Abstract

The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of particle is generated. We also indicate, that in the case of spatial coordinates commuting in Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces.

arXiv comment14 pages, 2 figures, v2: three references added, v3: accepted for publication in Physical Review D, v4: the page numbers for all references in preprint version are provided

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Cited by in corpus (23)

• Scalar Field Theory on Non-commutative Snyder Space-Time
• Newton's Equation on the kappa space-time and the Kepler problem
• Parameters of noncommutativity in Lie-algebraic noncommutative space
• Classical dynamics on curved Snyder space
• A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
• Classical mechanics of many particles defined on canonically deformed nonrelativistic space-time
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Noncommutative Geometry and Fluid Dynamics
• Group theoretical construction of planar Noncommutative Phase Spaces
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Generalized twist deformations of Poincare and Galilei Hopf algebras
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Twist deformations of Newton-Hooke Hopf algebras
• Noncommutative Brownian motion
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Generating of additional force terms in Newton equation by twist-deformed Hopf algebras and classical symmetries
• Para-Galilean versus Galilean Noncommutative Phase spaces
• Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space
• Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system
• New parameters of Non-commutativity in Quantum Mechanics
• Equivalent forces in Newton equation from twist deformations and noninertial coordinate frames
• (2 +1)-dimensional Duffin-Kemmer-Petiau oscillator under a magnetic field in the presence of a minimal length in the noncommutative space
• Twist deformation of doubly enlarged Newton-Hooke Hopf algebra