Spectrum of Schroedinger field in a noncommutative magnetic monopole

TL;DR

This paper computes the energy spectrum of a Schrödinger particle on a noncommutative sphere with a magnetic monopole, revealing how noncommutativity affects the spectral properties and monopole quantization.

Contribution

It provides a field-theoretic analysis of a noncommutative monopole system, connecting the Hamiltonian to angular momentum with a nontrivial scaling, and clarifies monopole quantization via Seiberg-Witten mapping.

Findings

Energy spectrum derived for noncommutative monopole system

Hamiltonian related to angular momentum with scaling factor

Monopole quantization linked to Seiberg-Witten mapped fields

Abstract

The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged Schroedinger field coupled to a noncommutative U(1) gauge field is identified. It is shown that the Hamiltonian is essentially the angular momentum squared of the particle, but with a nontrivial scaling factor appearing, in agreement with the first-quantized canonical treatment of the problem. Monopole quantization is recovered and identified as the quantization of a commutative Seiberg-Witten mapped monopole field.