2006/10/31 by Hajime Aoki, Satoshi Iso, Toshiharu Maeda · 2 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Artificial intelligence #Black Holes and Theoretical Physics #Chemistry #Computer science #Dirac (video compression format) #Dirac operator #Fuzzy logic #Magnetic monopole #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevd.75.085021
published as Phys.Rev.D75:085021,2007 · Latex2e, 37 pages, 3 figures
arxiv created 2007/03/23 · openalex publication_date 2007/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In previous papers, we studied 't Hooft-Polyakov (TP) monopole configurations in U(2) gauge theory on the fuzzy 2-sphere, and showed that they have nonzero topological charges in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provides meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that configuration space can be classified into topological sectors. We further calculate the spectrum of the GW Dirac operator in TP monopole backgrounds, and consider the index theorem in these cases.