Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations

  title={Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations},
  author={Maria Gargiulo and Mairi Sakellariadou and Giuseppe Vitiello},
  journal={Journal of Physics: Conference Series},
In this report we show that neutrino mixing is intrinsically contained in Connes’ noncommutatives pectral 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 the algebra and neutrino mixing within noncommutative spectral geometry

We study the 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

Constraining the noncommutative spectral action via astrophysical observations.

Observations of pulsar timings are used, assuming that no deviation from general relativity has been observed, to constrain the gravitational sector of this theory and the bounds on the coupling constants remain rather weak.

Noncommutative spectral geometry, algebra doubling and the seeds of quantization

is presented. It is shown that the doubling of the algebra is related to dissipation and to the gauge structure of the theory, the gauge eld acting as a reservoir for the matter eld. In a regime of

Quantum field theory of three flavor neutrino mixing and oscillations with CP violation

We study in detail the quantum field theory of mixing among three generations of Dirac fermions (neutrinos). We construct the Hilbert space for the flavor fields and determine the generators of the

Inflation in models with conformally coupled scalar fields: An application to the noncommutative spectral action

Slow-roll inflation is studied in theories where the inflaton field is conformally coupled to the Ricci scalar. In particular, the case of Higgs field inflation in the context of the noncommutative


I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most

Cosmology and the Noncommutative approach to the Standard Model

We study cosmological consequences of the noncommutative approach to the standard model of particle physics. Neglecting the nonminimal coupling of the Higgs field to the curvature, noncommutative

Quantum Field Theory of Fermion Mixing

The fermion mixing transformations are studied in the quantum field theory framework. In particular neutrino mixing is considered and the Fock space of definite flavor states is shown to be unitarily

Conceptual explanation for the algebra in the noncommutative approach to the standard model.

The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a

Particle Physics from Almost Commutative Spacetimes

Our aim in this review paper is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical