Universal Formula for Noncommutative Geometry Actions: Unification of Gravity and the Standard Model

Ali H. Chamseddine and Alain Connes
Phys. Rev. Lett. 77, 4868 – Published 9 December 1996
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Abstract

A universal formula for an action associated with a noncommutative geometry, defined by a spectral triple (A,H,D), is proposed. It is based on the spectrum of the Dirac operator and is a geometric invariant. The new symmetry principle is the automorphism of the algebra A which combines both diffeomorphisms and internal symmetries. Applying this to the geometry defined by the spectrum of the standard model gives an action that unifies gravity with the standard model at a very high energy scale.

  • Received 17 June 1996

DOI:https://doi.org/10.1103/PhysRevLett.77.4868

©1996 American Physical Society

Authors & Affiliations

Ali H. Chamseddine1,2 and Alain Connes2

  • 1Theoretische Physik, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
  • 2I.H.E.S., F-91440 Bures-sur-Yvette, France

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Vol. 77, Iss. 24 — 9 December 1996

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