Brêve défense de l'intérêt de la géométrie non commutative comme outil pour comprendre le Modèle Standard
To [build] our comparison of atomic and particle physics, we need the underlying theory, which is noncommutative geometry... Indeed it derives the complicated Yang-Mills-Higgs ansatz from first principles: geometry and general relativity... this derivation implies constraints of which the most spectacular certainly is: the scalar representation is computed not chosen. And for the standard model, this computation produces, on the nose, the scalar representation chosen by experiment...Intuitively noncommutative geometry does to curved space(time) what quantum mechanics did to (flat) phase space, equipping space with an uncertainty relation...In [the spectral non commutative] derivation, the entire Yang-Mills-Higgs action pops up as a companion to the Einstein-Hilbert action, just like the magnetic field pops up as a companion to the electric field, when the latter is generalized to Minkowskian geometry, i.e. special relativity. And [the spectral non commutative] derivation implies constraints. On the discrete side, besides being able to compute the scalar representation ... we get constraints on the choice of the group G and of the fermionic representation.
Thomas Schücker, The noncommutative standard model, post- and predictions, 29/03/2010