Le principe d'action spectrale dans la géométrie non commutative : une grande échelle de Jacob lancée entre Fermi et Planck
I understand noncommutative spectral models as the kind of models initiated by Connes et al.Does the absence of Wick rotation from noncommutative spectral models back to Minkowski signature can cast some doubts on the physical pertinence of the principle of spectral action that make it possible to connect the abstract dynamics and grand symmetric algebras uncovered by noncommutative geometry with the phenomenology of particle physics?This would help me to know if the artcraft (or wizardry) of model building oriented noncommutative could be useful to understand something beyond the Standard Model.
Laboussoleestmonpays, Absence of Wick rotation from noncommutative spectral models back to Minkowski signature 27/08/2013
We work in Euclidean rather than Lorentz signature, leaving as an important problem the Wick rotation back to the Minkowski signature. For a formulation in Minkowski signature see .
A. Connes et Mathilde Marcolli, Noncommutative Geometry, Quantum Fields and Motives 2007
The commonly assumed background of special relativity is a Minkowski space-time, i.e. a ﬂat four-dimensional manifold equipped with a Lorentzian signature. When generalizing the theory of relativity (GR) by the introduction of curvature in the actual space-time, the Minkowski manifold is typical of all tangent spaces to the curved manifold. Minkowski spacetime as such does in a sense not exist, but is the asymptotic form of any real space-time when all kinds of matter/energy are taken out. This simple view, however, hides a puzzling feature. A Minkowski manifold is not the most general undiﬀerentiated ﬂat four-dimensional manifold, because of the light cones, i.e. of the Lorentzian signature. The structure of the light cones picks out a bunch of directions stemming from any given event in the manifold (the time-like worldlines) which cannot be confused with the rest. Where does this symmetry diminution come from? Indeed the most general four-dimensional manifold should be Euclidean: perfect isotropy and homogeneity. This is the question for which I shall try to ﬁnd an answer in the present work.
The hidden geometrical structure of the standard model of particle physics was discovered by Connes using non-commutative geometry[C]. His model suﬀers from two defects from the physical point of view: ﬁrstly that the spacetime metric is Euclidean, and secondly that each particle appears four times, not once[LMMS, GIS]. The purpose of this paper is to give the analogous geometrical framework for the standard model with Lorentzian signature which also, at the same time, solves the particle quadrupling problem. This model allows the introduction of neutrino masses using the see-saw mechanism.
John W. Barrett, A Lorentzian version of the non-commutative geometry of the standard model of particle physics 6/11/2006