Dirac monopoles from the Matsumoto non-commutative spheres

TL;DR

This paper demonstrates that Matsumoto's non-commutative three-sphere serves as a quantum Hopf bundle over the classical two-sphere, with a canonical connection matching the Dirac magnetic monopole.

Contribution

It establishes a geometric interpretation of Matsumoto's non-commutative three-sphere as a quantum Hopf bundle with a canonical connection.

Findings

The non-commutative three-sphere is a total space of a quantum Hopf bundle.

A canonical connection on this bundle is constructed.

The connection coincides with the Dirac magnetic monopole.

Abstract

It is shown that the non-commutative three-sphere introduced by Matsumoto is a total space of the quantum Hopf bundle over the classical two-sphere. A canonical connection is constructed, and is shown to coincide with the standard Dirac magnetic monopole.