Noncommutative Particles in Curved Spaces

TL;DR

This paper develops a covariant formulation of noncommutative mechanics in curved spacetime, treating the noncommutativity parameter as a dynamical variable with conjugate momentum, and generalizes previous relativistic models.

Contribution

It introduces a covariant, diffeomorphism-invariant noncommutative mechanics model in curved space with a dynamical noncommutativity parameter.

Findings

Derived covariant equations of motion in D=10 curved spacetime.

Established invariance under diffeomorphisms.

Generalized recent relativistic noncommutative models.

Abstract

We present a formulation in a curved background of noncommutative mechanics, where the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity having a canonical conjugate momentum. We introduced a noncommutative first-order action in D=10 curved spacetime and the covariant equations of motions were computed. This model, invariant under diffeomorphism, generalizes recent relativistic results.