), is ana extensionmodel ofbased theon [[Standardnoncommutative Modelgeometry]] minimallythat coupled tounifies a modified form of [[general relativity]] expressed inwith the framework of [[noncommutativeStandard geometryModel]].In that sense, it unifies gravity and particle physics in a(extended commonwith mathematicalright-handed frameworkneutrinos).
The model postulates that space-time is mildlythe non-commutativeproduct byof tensoring the continuousa 4-dimensional spacecompact spin manifold <math>\mathcal{M}</math> by a finite non-commutative space <math>\mathcal{F}</math>. The full Lagrangian (ain matrixEuclidean algebrasignature) of the [[Standard model]] minimally coupled to gravity is obtained as pure gravity over that product space. It is therefore close in spirit to [[Kaluza-Klein theory]] but without the problem of massive tower of states.
The [[Lagrangian]] of the full [[Standard Model]] minimally coupled to gravity is obtained by the action of pure gravity over that tensored space.
The parameters of the model live at unification scale and physical predictions are obtained by running the parameters down through [[Renormalization]].
It is worth stressing that it is more than a simple reformation of the [[Standard Model]]. This unification implies a few constraints on the parameters of the Standard Model. For example, unlike [[Quantum Field Theory]], in [[noncommutative geometry]] the scalar sector is strongly constrained.
It is worth stressing that it is more than a simple reformation of the [[Standard Model]]. For example, the scalar sector and the fermions representations are more constrained than in [[Effective field theory]].
