2002/07/28 by Brian P Dolan, Brian P. Dolan, Charles Nash +1 · 13 citations
Physics and Astronomy · #Atiyah–Singer index theorem #Electroweak interaction #Fermion #Grassmannian #Matrix (chemical analysis) #Neutrino Physics Research #Noncommutative and Quantum Gravity Theories #Quantum Chromodynamics and Particle Interactions #Space (punctuation) #Spectrum (functional analysis) #Unitary state #hep-th
paper · pdf · doi:10.1088/1126-6708/2002/07/057
published in Journal of High Energy Physics 2002(07), 057 (Springer Nature) · 22 pages, no figures
openalex publication_date 2002/07/28 · arxiv created 2002/09/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Atiyah-Singer index theorem is investigated on various compact manifolds which admit finite matrix approximations (``fuzzy spaces'') with a view to applications in a modified Kaluza-Klein type approach in which the internal space consists of a finite number of points. Motivated by the chiral nature of the standard model spectrum we investigate manifolds that do not admit spinors but do admit Spinc structures. It is shown that, by twisting with appropriate bundles, one generation of the electroweak sector of the standard model, including a right-handed neutrino, can be obtained in this way from the complex projective space \CP2. The unitary Grassmannian U(5)/(U(3)× U(2)) yields a spectrum that contains the correct charges for the Fermions of the standard model, with varying multiplicities for the different particle states.