Noncommutative geometry of phase space

TL;DR

This paper introduces a novel approach to noncommutative geometry that focuses on phase space, extending classical dualities to incorporate noncommutative structures in momentum and position variables.

Contribution

It proposes a phase-space based noncommutative geometry framework, extending the duality between tangent and cotangent bundles to noncommutative settings.

Findings

Develops a phase-space noncommutative geometry model

Extends classical duality to noncommutative algebra of forms

Provides a new perspective on noncommutative geometric structures

Abstract

A version of noncommutative geometry is proposed which is based on phase-space rather than position space. The momenta encode the information contained in the algebra of forms by a map which is the noncommutative extension of the duality between the tangent bundle and the cotangent bundle.