1999/04/26 by J. A. Mignaco, C. Sigaud, A. R. da Silva +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Hilbert space #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Pure mathematics #Quantum optics and atomic interactions #Rigged Hilbert space #Space (punctuation) #Spectral triple #Spinor #Unitary operator #hep-th
paper · pdf · doi:10.1142/s0129055x01000582
published as Rev.Math.Phys.13:1-28,2001 · 57 pages, LATEX
arxiv created 1999/04/26 · openalex publication_date 2001/01/01 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work we examine generalized Connes–Lott models, with C⊕C as finite algebra, over 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.