Aharonov-Bohm Effect in Noncommutative Spaces

TL;DR

This paper investigates the Aharonov-Bohm effect within noncommutative quantum spaces, deriving phase shifts and establishing bounds on noncommutativity parameters through path integral methods.

Contribution

It introduces a path integral formulation for the Aharonov-Bohm effect in noncommutative spaces and calculates gauge-invariant phase corrections.

Findings

Gauge-invariant phase shift corrections due to noncommutativity

Numerical bounds on the noncommutativity parameter

Modified propagation amplitude in noncommutative quantum mechanics

Abstract

The Aharonov-Bohm effect on the noncommutative plane is considered. Developing the path integral formulation of quantum mechanics, we find the propagation amplitude for a particle in a noncommutative space. We show that the corresponding shift in the phase of the particle propagator due to the magnetic field of a thin solenoid receives certain gauge invariant corrections because of the noncommutativity. Evaluating the numerical value for this correction, an upper bound for the noncommutativity parameter is obtained.