Magnetic monopoles and symmetries in noncommutative space

TL;DR

This paper reviews the algebraic structures and symmetries of magnetic monopoles within quantum mechanics on noncommutative space, highlighting their broader applicability and underlying mathematical richness.

Contribution

It introduces a detailed analysis of magnetic monopoles in noncommutative quantum space, revealing complex symmetries applicable to various physical models.

Findings

Rich algebraic structures generate symmetries in monopole models

Results applicable to both noncommutative and ordinary quantum mechanics

Enhanced understanding of monopole-related symmetries in quantum physics

Abstract

In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized in different physical contexts. Even though are we focused on quantum mechanics in noncommutative space $\textbf{R}_\lambda^3$, the results can be reconstructed in ordinary quantum mechanics in $\textbf{R}^3$ as well.