Aharonov-Bohm effect in a Class of Noncommutative Theories

Abstract

The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $θ$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schrödinger-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 $θ$.

10 pages