Connes-Lott model building on the two-sphere

TL;DR

This paper explores generalized Connes-Lott models on the two-sphere, incorporating nontrivial topological structures like magnetic monopoles through spectral triples and twisted spinor bundles.

Contribution

It introduces a novel construction of spectral triples on the two-sphere that include topologically non-trivial modules and monopole configurations.

Findings

Successful construction of spectral triples with magnetic monopoles.

Extension of the Hilbert space to include particle and anti-particle fields.

Demonstration of topologically non-trivial modules over S^2.

Abstract

In this work we examine generalized Connes-Lott models on the two-sphere. The Hilbert space of the continuum spectral triple is taken as the space of sections of a twisted spinor bundle, allowing for nontrivial topological structure (magnetic monopoles). The finitely generated projective module over the full algebra is also taken as topologically non-trivial, which is possible over $S^2$. We also construct a real spectral triple enlarging this Hilbert space to include "particle" and "anti-particle" fields.