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.

14 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

References in corpus (8)

• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• From noncommutative kappa-Minkowski to Minkowski space-time
• Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Canonical and Lie-algebraic twist deformations of Galilei algebra
• Equations of motion, Noncommutativity and Quantization
• Lagrangian and Noncommutativity
• Noncommutative Lagrange Mechanics

Cited by in corpus (10)

• Newton's Equation on the kappa space-time and the Kepler problem
• Classical mechanics of many particles defined on canonically deformed nonrelativistic space-time
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• 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
• New parameters of Non-commutativity in Quantum Mechanics
• (2 +1)-dimensional Duffin-Kemmer-Petiau oscillator under a magnetic field in the presence of a minimal length in the noncommutative space
• Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system