Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential

TL;DR

This paper investigates how noncommutative spacetime modifies the Aharonov-Bohm effect for relativistic spin 1/2 particles in 2+1 dimensions, revealing corrections to scattering amplitudes and cross sections.

Contribution

It introduces a novel perturbative approach around the exact commutative solution to handle divergences caused by noncommutativity.

Findings

Derived corrections to the scattering amplitude.

Calculated modifications to differential cross sections.

Analyzed effects in the small-flux limit.

Abstract

In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due to the noncommutativity of spacetime in $2 + 1$ dimensions. The noncommutativity gives rise to a correction to the Aharonov-Bohm potential which is highly singular at the origin, producing divergences in a perturbative expansion around the usual solution of the free Dirac equation. This problem is surmounted by using a perturbative expansion around the exact solution of the \textit{commutative} Aharonov-Bohm problem. We calculate, in this setting, the scattering amplitude and the corrections to the differential and total cross sections for a spin 1/2 particle, in the small-flux limit.