On Noncommutative Classical Mechanics

TL;DR

This paper explores the structure of noncommutative classical mechanics by analyzing the noncommutative Poisson algebra of observables, linking large-scale noncommutativity with quantum-scale phenomena and UV/IR mixing.

Contribution

It introduces a framework for noncommutative classical mechanics based on a noncommutative Poisson algebra, connecting classical and quantum noncommutativity.

Findings

Noncommutative Poisson algebra structure identified

Classical systems with noncommutative potentials analyzed

Potential links between large-scale and quantum-scale noncommutativity proposed

Abstract

In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, \cite{1}. I treat some classical systems with various potentials and some Physical interpretations are given concerning the presence of noncommutativity at large scales (Celeste Mechanics) directly tied to the one present at small scales (Quantum Mechanics) and its possible relation with UV/IR mixing.