Doubling of the Algebra and Neutrino Mixing within Noncommutative Spectral Geometry

TL;DR

This paper explores how the algebra doubling in noncommutative spectral geometry leads to neutrino mixing and offers insights into the standard model's geometric foundation.

Contribution

It demonstrates the connection between algebra doubling and neutrino mixing within the noncommutative spectral geometry framework, linking it to deformed Hopf algebras.

Findings

Algebra doubling is linked to neutrino mixing.

Bogoliubov transformations emerge from the algebra structure.

Provides a geometric explanation for standard model features.

Abstract

We study physical implications of the doubling of the algebra, an essential element in the construction of the noncommutative spectral geometry model, proposed by Connes and his collaborators as offering a geometric explanation for the standard model of strong and electroweak interactions. Linking the algebra doubling to the deformed Hopf algebra, we build Bogogliubov transformations and show the emergence of neutrino mixing.