Noncommutative Quantum Scattering in a Central Field

TL;DR

This paper investigates how noncommutative geometry affects quantum elastic scattering in a central field, deriving formulas and analyzing the impact on differential cross-sections at different energy scales.

Contribution

It provides new formulas for noncommutative scattering and analyzes the effects of noncommutativity on cross-sections and particle distribution.

Findings

At high energy, noncommutative scattering matches commutative results.

Small noncommutativity causes azimuthal redistribution of particles.

Total cross-section remains unchanged by noncommutativity.

Abstract

In this paper the problem of noncommutative elastic scattering in a central field is considered. General formulas for the differential cross-section for two cases are obtained. For the case of high energy of an incident wave it is shown that the differential cross-section coincides with that on the commutative space. For the case in which noncommutativity yields only a small correction to the central potential it is shown that the noncommutativity leads to the redistribution of particles along the azimuthal angle, although the whole cross-section coincides with the commutative case.