Classical q-deformed dynamics

TL;DR

This paper explores a q-deformation of classical mechanics using quantum group algebra and non-commutative calculus, extending classical kinetic equations to include q-deformed dynamics.

Contribution

It introduces a novel q-deformed Poisson bracket framework to extend classical dynamics within quantum group theory.

Findings

Derived q-deformed kinetic equations including Fokker-Planck and Kramers equations.

Established a mathematical foundation for q-deformed classical mechanics.

Explored implications of q-deformation in kinetic theory and classical regimes.

Abstract

On the basis of the quantum q-oscillator algebra in the framework of quantum groups and non-commutative q-differential calculus, we investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized q-deformed dynamics in the classical regime. In this framework, classical q-deformed kinetic equations, Kramers and Fokker-Planck equations, are also studied. Pacs: 05.20.Dd, 45.20.-d, 02.20.Uw Keywords: Kinetic theory, q-deformed classical mechanics, quantum groups, quantum algebras