Almost-Commutative Geometry, massive Neutrinos and the Orientability Axiom in KO-Dimension 6

Abstract

In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was that at least the orientability axiom of noncommutative geometry [5,6] may not be obeyed by the underlying geometry. In this publication we review three internal geometries, all three failing to meet the orientability axiom of noncommutative geometry. They will serve as examples to illustrate the nature of this lack of orientability. We will present an extension of the minimal standard model found in [7] by a right-handed neutrino, where only the sub-representation associated to this neutrino is not orientable.

References in corpus (5)

• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Noncommutative Geometry and the standard model with neutrino mixing
• On a Classification of Irreducible Almost-Commutative Geometries IV
• Composite Dark Matter with Invisible Light from Almost-Commutative Geometry
• Krajewski diagrams and spin lifts

Cited by in corpus (4)

• On a Classification of Irreducible Almost-Commutative Geometries IV
• Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
• On the noncommutative standard model
• The Inverse Seesaw Mechanism in Noncommutative Geometry