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

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.

arXiv comment15 pages LaTeX

References in corpus (5)

• The Spectral Action Principle
• The Standard Model Effective Potential at Two Loops
• On the universal Chamseddine-Connes action 1. Details of the action computation
• Remarks on Alain Connes' approach to the standard model
• Unification of Gravity and Yang-Mills-Higgs Gauge Theories

Cited by in corpus (6)

• The standard model in noncommutative geometry and fermion doubling
• On summability of distributions and spectral geometry
• Noncommutative Geometry for Pedestrians
• Mirror Fermions in Noncommutative Geometry
• Non-commutative geometry and the standard model vacuum
• Noncommutative Yang-Mills and Noncommutative Relativity: A Bridge Over Trouble Water