Testing spatial noncommutativiy via the Aharonov-Bohm effect

TL;DR

This paper investigates how noncommutative space could be detected through modifications in the Aharonov-Bohm effect, predicting measurable diffraction patterns and cross sections that could reveal space noncommutativity at high energies.

Contribution

It introduces a method to detect space noncommutativity via the Aharonov-Bohm effect, including calculations of diffraction patterns and scattering cross sections with a derived energy bound.

Findings

Noncommutative space induces measurable diffraction patterns.

A bound of approximately 10 TeV is established for noncommutative effects.

Potential for experimental detection in high-energy scattering experiments.

Abstract

The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives non-trivial kinematical corrections that will produce a diffraction pattern even when the magnetic flux is quantized. The scattering problem is also formulated, and the differential cross section is calculated. Our results can be extrapolated to high energy physics and the bound $\theta \sim [ 10 {TeV}]^{-2}$ is found. If this bound holds, then noncommutative effects could be explored in scattering experiments measuring differential cross sections for small angles. The bound state Aharonov- Bohm effect is also discussed.