Noncommutative Geometry as the Key to Unlock the Secrets of Space-Time

Abstract

I give a summary of the progress made on using the elegant construction of Alain Connes noncommutaive geometry to explore the nature of space-time at very high energies. In particular I show that by making very few natural and weak assumptions about the structure of the noncommutative space, one can deduce the structure of all fundamental interactions at low energies.

Contribution to a special volume in honor of Alain Connes in occasion of his 60th birthday. To be published in the Proceedings series of the Clay Mathematics Institute. Editors E. Blanchard et al

References in corpus (5)

• Gravity and the standard model with neutrino mixing
• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Noncommutative Geometry and the standard model with neutrino mixing
• Why the Standard Model
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

Cited by in corpus (4)

• Resilience of the Spectral Standard Model
• Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
• Early Universe models from Noncommutative Geometry
• Quantum theory, gravity, and the standard model of particle physics : using the hints of today to build the final theory of tomorrow