Constraints on the scalar potential from spectral action principle

Abstract

Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix valued functions on space-time, the standard model of particle physics can be reconstructed out of a few basic principles. Following these ideas, we investigate the general case of models arising from matrices and give the resulting constraints on the scalar potential and gauge couplings constants, as well as some relations between fermionic and bosonic masses.

Latex file, 21 pages and 8 eps figures included

References in corpus (11)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• A Universal Action Formula
• General Relativity in terms of Dirac Eigenvalues
• On summability of distributions and spectral geometry
• On the universal Chamseddine-Connes action 1. Details of the action computation
• Anomaly Cancellation and gauge group of the standard model in NCG
• Non-commutative Geometry Beyond the Standard Model
• The Scalar Potential in Noncommutative Geometry
• Discrete spectral triples and their symmetries

Cited by in corpus (2)

• On a Classification of Irreducible Almost-Commutative Geometries IV
• On a Classification of Irreducible Almost Commutative Geometries