Le boson de Higgs sait qu'il est un boson de jauge non commutatif et un possible portail vers un nouveau programme de grande unification (Chapitre final)
Qu'est-ce que le boson de Higgs sait que nous ne sav(i)ons pas?La grande unification retrouvée (?)
December 1, 2010 at 7:17 am
“I find it more likely that some major new ideas about the relationship between internal and space-time symmetry are still needed.”
Don’t we have them already in noncommutative geometry ? (According to Alain Connes, NCG allows for breaking the chains of the Coleman-Mandula theorem)...
Commentaire à propos du billet: A Geometric Theory of Everything, sur le blog Not Even Wrong, 17/11/2010
Or donc, le champ des possibles qui s'offre aujourd'hui aux constructeurs des théories physiques futures pour unifier les interactions fondamentales est désormais beaucoup plus contraint grâce à la découverte du (et aux mesures faites sur le) boson de Higgs. Néanmoins il est toujours riche de potentialités que la géométrie noncommutative et le principe d'action spectrale semblent particulièrement aptes à faire émerger. C'est du moins ce que nous allons tenter d'illustrer maintenant avec l'extrait suivant tiré du plus récent article phénoménologique sur le sujet à notre connaissance :
Noncommutative geometry allows to handle a large variety of geometrical frameworks from a totally algebraic point of view. In particular it is very useful in the derivation of models in high energy physics, such as the Yang-Mills gauge theories. In the current state the noncommutative geometry structure of gauge theories is understood to be an “almost commutative” geometry, i.e. the product of continuous geo-metry, representing space-time, times an internal algebra of finite dimensional matrix. In this geometric framework the spectral action principle enables the retrieval of the full standard model of high energy physics, including the Higgs field: the standard model is put on the same footing as geometrical general relativity making it a possible unification with gravity. In fact the application of noncommutative geometry to gauge theories of strong and electroweak forces is a very original way to fully geometrize the interaction of elementary particles. Furthermore it has been shown that it is possible to extend the standard model by including an additional singlet scalar field that stabilizes the running coupling constants of the Higgs field. This singlet scalar field is closely related to the right-handed Majorana neutrinos, conferring them mass, and leading to the prediction of the seesaw mechanism which explains the large difference between the masses of neutrinos and those of the other fermions. A recent model shows the possibility of a further extension, going one step higher in the construction of the noncommutative manifold, in a sort of noncommutative geometry grand unification: here it is pointed out that there could be a “next level” in noncommutative geometry, intertwined with the Riemannian and spin structure of spacetime, where the singlet-scalar field rises. Accordingly it naturally appears at high scale, near to the Planck scale.
Agostino Devastato, Spectral Action and Gravitational effects at the Planck scale 20/09/2013
The assumption that space-time is a noncommutatirave space formed as a product of a continuous four dimensional manifold times a finite space predicts, almost uniquely, the Standard Model with all its fermions, gauge fields, Higgs field and their representations. A strong restriction on the noncommutative space results from the first order condition which came from the requirement that the Dirac operator is a differential operator of order one. Without this restriction, invariance under inner automorphisms requires the inner fluctuations of the Dirac operator to contain a quadratic piece expressed in terms of the linear part. We apply the classification of product noncommutative spaces without the first order condition and show that this leads immediately to a Pati-Salam SU(2)R⊕SU(2)L⊕SU(4) type model which unifies leptons and quarks in four colors. Besides the gauge elds, there are 16 fermions in the (2; 2; 4) representation, fundamental Higgs fields in the (2; 2; 1), (2; 1; 4) and (1; 1; 1 + 15) representations. Depending on the precise form of the initial Dirac operator there are additional Higgs fields which are either composite depending on the fundamental Higgs fields listed above, or are fundamental themselves. These additional Higgs fields break spontaneously the Pati-Salam symmetries at high energies to those of the Standard Model.
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom, Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification 2013
As opposed to the original motivation, suggested by the phenomenological Ginzburg-Landau theory of second order phase transitions, where φ is an effective scalar field ..., it recieves [in noncommutative geometry] a completely different status as a connexion.. Thus, the Higgs field is here given a deep geometric interpretation ..., having its origin ... in [the fine structure of spacetime at the electroweak scale, namely a] virtual space consisting of two points, which by means of the [Yukawa couplings forming the matrix elements of an] associated Dirac operator can be equipped with a kind of discrete metric structure; ... now the Higgs field has become a dynamical agent since through the spectral action also its kinetic term is generated... noncommutative geometry yields the crucial insight that - before spontaneous symmetry breaking - all elementary fields of integer spin s = 0, 1, 2 are gauge fields !
Gerhard Grensing, Structural Aspects of Quantum Field Theory and Noncommutative Geometry, 2012
The discovery that confinement could be found in the strong coupling limit of quantum chromodynamics based on the “color” gauge group SU(3) led to tentative Grand Unification schemes where electroweak and strong interaction could be unified in a simple gauge group G containing SU(2)×U(1)×SU(3). Breaking occurs through vacuum expectation values of scalar fields and unification is apparent at high energies because, while the renormalization group makes the small gauge coupling of U(1) increase logarithmically with the energy scale, the converse is true for the asymptotically free non abelian gauge groups. Originally the BEH mechanism was conceived to unify the theoretical description of longrange and short-range forces. The success of the electroweak theory made the mechanism a candidate for further unification. Grand unification schemes, where the scale of unification is pushed close to the scale of quantum gravity effects, strengthen the believe in a still larger unification that would include gravity. This trend towards unification received a further impulse from the developments of string theory and from its connection with eleven-dimensional supergravity.The latter is then often viewed as a classical limit of a hypothetical M-theory into which all perturbative string theories would merge to yield a comprehensive theory of “all” interactions. Such vision may be premature. Quite apart from obvious philosophical questions raised by a “theory of everything” formulated in the present framework of theoretical physics, the transition from perturbative string theory to its M-theory generalization hitherto stumbles on the treatment of non perturbative gravity. This might well be a hint that new conceptual elements have to be found to cope with the relation between gravity and quantum theory and which might not be directly related to the unification program.
François Englert, Broken symmetry and Yang-Mills theory 2004