The Kepler problem and non commutativity

TL;DR

This paper explores how noncommutative geometry affects the Kepler problem, revealing that tiny noncommutative parameters could lead to observable large-scale effects, linking quantum scale modifications to macroscopic phenomena.

Contribution

It introduces a symplectic structure compatible with noncommutative quantum mechanics into the Kepler problem, showing potential observable effects of noncommutativity at solar system scales.

Findings

Noncommutative parameter of order 10^{-58} m^2 affects planetary motion.

Noncommutative effects could be observable at large scales due to UV/IR mixing.

Modifications at quantum scales influence macroscopic physics.

Abstract

We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable corrections to the movement of the solar system. In this way, modifications in the physics of smaller scales implies modifications at large scales, something similar to the UV/IR mixing.