Noncommutative geometry induced by spin effects

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 $\overrightarrow{S}$ 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 written in terms of noncommutative coordinates which indicates that bound states are particular cases in this procedure. Concerning confined or bounded particles in this noncommutative domain, we verify that the kinetic energy is modified by a deformation factor. Finally, we discuss perspectives.

Figure 1

Plot of electrostatics force $\widehat{F}$ versus the distance $r$.