Space-Time from the spectral point of view

Abstract

We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new paradigm to model space-time whose fine structure can be encoded by a finite geometry. The classification of the irreducible finite geometries of KO-dimension 6 singles out a ``symplectic--unitary" candidate F, which when used as the fine texture of space-time delivers from pure gravity on M x F the Standard Model coupled to gravity and, once extrapolated to unification scale, gives testable predictions.

19 pages. To appear in the Proceedings of the 12th Marcel Grossmann meeting

References in corpus (7)

• 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
• Inner fluctuations of the spectral action
• Supersymmetric QCD and noncommutative geometry
• Non-compact spectral triples with finite volume

Cited by in corpus (6)

• Spectral action, Weyl anomaly and the Higgs-Dilaton potential
• Clifford Algebras and Spinors
• A new algebraic structure in the standard model of particle physics
• The $x_i$-eigenvalue problem on some new fuzzy spheres
• Field Theory with Coordinate Dependent Noncommutativity
• Nilpotence and the generalized uncertainty principle(s)