Classical dynamics in deformed spaces

TL;DR

This paper explores a three-parameter deformation of classical Poisson brackets, modeling dynamics in 'quantized spaces', and provides a detailed description of particle motion in the deformed Kepler-Coulomb problem.

Contribution

It introduces a new three-parameter deformation of Poisson brackets and analyzes the resulting classical dynamics in the context of 'quantized spaces.'

Findings

Describes particle motion in the deformed Kepler-Coulomb problem.

Links classical deformations to quantum space models.

Provides mathematical framework for deformed classical mechanics.

Abstract

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the motion of a particle in the corresponding Kepler-Coulomb problem.