Magnetic monopoles in noncommutative quantum mechanics

TL;DR

This paper explores how a natural generalization of the state space in noncommutative quantum mechanics introduces magnetic monopoles, providing new insights into their theoretical properties and relations like the Dirac quantization condition.

Contribution

It presents a novel approach to incorporate magnetic monopoles into quantum mechanics via a generalized Hilbert space, applicable to both noncommutative and ordinary frameworks.

Findings

Magnetic monopoles naturally emerge from the generalized Hilbert space structure.

The approach offers a new perspective on the Dirac quantization condition.

Investigation of Coulomb potential dynamics with monopoles included.

Abstract

We discuss certain generalization of the Hilbert space of states in noncommutaive quantum mechanics that, as we show, introduces magnetic monopoles into the theory. Such generalization arises very naturally in the considered model, but can be easily reproduced in ordinary quantum mechanics as well. This approach offers a different viewpoint on the Dirac quantization condition and other important relations for magnetic monopoles. We focus mostly on the kinematic structure of the theory, but investigate also a dynamical problem (with the Coulomb potential).