Noncommutative geometry induced by spin effects

TL;DR

This paper explores how noncommutative spacetime effects, induced by a background spin-related field, influence simple physical systems, revealing spin-orbit coupling and modifications to kinetic energy in a noncommutative geometric framework.

Contribution

It introduces a model linking noncommutative geometry effects to spin structures, deriving new spin-orbit coupling terms and energy modifications in simple systems.

Findings

Spin-orbit coupling emerges from noncommutative effects.

Kinetic energy is altered by a deformation factor.

Bound states are analyzed within this noncommutative framework.

Abstract

In this paper we study the nonlocal effects of noncommutative spacetime on simple physical systems. Our main point is the assumption that the noncommutative effects are consequences of a background field which generates a local spin structure. So, we reformulate some simple electrostatic models in the presence of a spin-deformation contribution to the geometry of the motion, and we obtain an interesting correlation amongst the deformed area vector, the 3D noncommutative effects and the usual spin vector given in quantum mechanics framework. Remarkably we can observe that a spin-orbit coupling term comes to light on the spatial sector of a potential wrote in terms of noncommutative coordinates what indicates that bound states are particular cases in this procedure. Concerning to confined or bounded particles in this noncommutative domain we verify that the kinetic energy is modified by a deformation factor. Finally, we discuss about perspectives.