Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-08-31
Int.J.Mod.Phys.D20:785-804,2011
Physics
High Energy Physics
High Energy Physics - Theory
11 pages; Invited contribution for Mario Castagnino's Festschrift, to be published in IJMPD
Scientific paper
10.1142/S021827181101913X
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 successful phenomenological model of particle physics. Noncommutative geometry states that close to the Planck energy scale, space-time has a fine structure and proposes that it is given as the product of a four-dimensional continuum compact Riemaniann manifold by a tiny discrete finite noncommutative space. The spectral action principle, a universal action functional on spectral triples which depends only on the spectrum of the Dirac operator, applied to this almost commutative product geometry, leads to the full Standard Model, including neutrino mixing which has Majorana mass terms and a see-saw mechanism, minimally coupled to gravity. It also makes various predictions at unification scale. I will review some of the phenomenological and cosmological consequences of this beautiful and purely geometrical approach to unification.
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