Aharonov-Bohm effect in a Class of Noncommutative Theories

TL;DR

This paper investigates the Aharonov-Bohm effect within a noncommutative framework, deriving exact solutions and analyzing how noncommutativity influences scattering properties, revealing gauge invariance and independence of the cross section from noncommutative parameters.

Contribution

It provides an exact solution to the noncommutative Aharonov-Bohm problem including spin effects, demonstrating gauge invariance and the independence of the differential cross section from noncommutative parameters.

Findings

The magnetic field remains gauge invariant at linear order in .

The Schrodinger-Pauli equation is separable despite anisotropy.

The differential cross section does not depend on the noncommutative parameter .

Abstract

The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $\theta$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schr\"odinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of $\theta$.