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

Marcin Daszkiewicz, Cezary J. Walczyk

Published 2008-02-25, updated 2009-01-27Version 4

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.