Testing spatial noncommutativity via the Aharonov-Bohm effect

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 nontrivial 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 $\ensuremath{\theta}\ensuremath{\sim}[10 \mathrm{TeV}{]}^{\ensuremath{-}2}$ 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.