On Connes' new principle of general relativity. Can spinors hear the forces of spacetime?

1996/12/23 by Lionel Carminati, Carminati, Lionel, Bruno Iochum +6 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9612228

15 pages LaTeX

arxiv created 1996/12/23 · openalex publication_date 1996/12/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Connes has extended Einstein's principle of general relativity to noncommutative geometry. The new principle implies that the Dirac operator is covariant with respect to Lorentz and internal gauge transformations and the Dirac operator must include Yukawa couplings. It further implies that the action for the metric, the gauge potentials and the Higgs scalar is coded in the spectrum of the covariant Dirac operator. This ``universal'' action has been computed by Chamseddine & Connes, it is the coupled Einstein-Hilbert and Yang-Mills-Higgs action. This result is rederived and we discuss the physical consequences.

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• The standard model in noncommutative geometry and fermion doubling

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