2006/05/31 by Alain Connes, Ali H. Chamseddine · 71 citations
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Dimension (graph theory) #Feynman diagram #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Quantum mechanics #Spectral triple #hep-th #math.OA #math.QA
paper · pdf · doi:10.1016/j.geomphys.2006.08.003
published in Journal of Geometry and Physics 57(1), 1-21 (Elsevier BV) · 18 pages, 4 figures Equation 1.6 corrected
arxiv created 2006/06/20 · openalex publication_date 2006/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove in the general framework of noncommutative geometry that the inner fluctuations of the spectral action can be computed as residues and give exactly the counterterms for the Feynman graphs with fermionic internal lines. We show that for geometries of dimension less or equal to four the obtained terms add up to a sum of a Yang-Mills action with a Chern-Simons action.