Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations

TL;DR

This paper demonstrates that neutrino mixing naturally arises within Connes' noncommutative spectral geometry framework through algebra doubling linked to Bogoliubov transformations, which cause the transition from mass to flavor vacuum states.

Contribution

It reveals a fundamental connection between algebra doubling in noncommutative geometry and neutrino oscillations, providing a geometric interpretation of neutrino mixing.

Findings

Neutrino mixing is embedded in noncommutative spectral geometry.

Algebra doubling relates to Bogoliubov transformations responsible for mixing.

Mass and flavor vacua are unitarily inequivalent.

Abstract

In this report we show that neutrino mixing is intrinsically contained in Connes' noncommutative spectral geometry construction, thanks to the introduction of the doubling of algebra, which is connected to the Bogoliubov transformation. It is known indeed that these transformations are responsible for the mixing, turning the mass vacuum state into the flavor vacuum state, in such a way that mass and flavor vacuum states are not unitary equivalent. There is thus a red thread that binds the doubling of algebra of Connes' model to the neutrino mixing.