A Variational Formulation of Symplectic Noncommutative Mechanics

TL;DR

This paper introduces a variational principle for noncommutative dynamical systems in configuration space, aiming to better understand the properties of classical and quantum noncommutative spaces.

Contribution

It proposes a new variational formulation in configuration space for noncommutative mechanics, extending previous work and facilitating analysis of noncommutative space properties.

Findings

Provides a variational principle for noncommutative systems

Helps elucidate properties of noncommutative space in classical and quantum contexts

Extends previous theoretical frameworks

Abstract

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [14]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.