On a classification of irreducible almost-commutative geometries V

Jureit, Jan-Hendrik; Stephan, Christoph A.

doi:10.1063/1.3167287

Cited by 10 publications

(17 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The KO dimension is an algebraic dimension which governs the commutation relations of the real structure J and the chirality . 6 has been carried out, 19 finding essentially the standard model with four summands in the matrix algebra. For an extensive study of this model we refer to Ref.…”

Section: Discussionmentioning

confidence: 99%

Massive neutrinos in almost-commutative geometry

Stephan

2007

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

Articles you may be interested inOn a classification of irreducible almost-commutative geometries V Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing On a classification of irreducible almost commutative geometries, a second helping In the noncommutative formulation of the standard model of particle physics by Chamseddine and Connes ͓Commun. Math. Phys. 182, 155 ͑1996͒, e-print hep-th/ 9606001͔, one of the three generations of fermions has to possess a massless neutrino. ͓C. P. Martin et al., Phys. Rep. 29, 363 ͑1998͒, e-print hep-th-9605001͔.This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix ͑PMNS matrix͒. But future experiments which may be able to detect neutrino masses directly and highprecision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straightforward way from the version of Chamseddine and Connes since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.

show abstract

Section: Discussionmentioning

confidence: 99%

Massive neutrinos in almost-commutative geometry

Stephan

2007

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…This relation not only appears in the context of SU (5) Grand Unified Theory, but is also a feature of SO(10) and E 6 theories[12],[13].…”

mentioning

confidence: 85%

“…Furthermore, we show that the demands can be met upon extending the SM with a copy of the representation 2 ⊗ 1 o , but this has consequences for the number of particle generations.We finally prove that the Minimal Supersymmetric Standard Model is not among the models that satisfy our constraints, but we pose a solution that is a slight extension of the MSSM. * Electronic address: T.vandenBroek@science.ru.nl † Electronic address: waltervs@math.ru.nl arXiv:1211.0825v2 [hep-th] 14 Jan 2013 such as [6,7,8,9,10] and also [11]. The approach we take in this article is to exploit some of the more recent developments (see [4]) to put constraints on all possible SM extensions.…”

mentioning

confidence: 99%

Going beyond the Standard Model with noncommutative geometry

Broek

Suijlekom

2013

J. High Energ. Phys.

View full text Add to dashboard Cite

The derivation of the full Standard Model from noncommutative geometry has been a promising sign for possible applications of the latter in High Energy Physics. Many believe, however, that the Standard Model cannot be the final answer. We translate several demands whose origin lies in physics to the context of noncommutative geometry and use these to put constraints on the fermionic content of models. We show that the Standard Model only satisfies these demands provided it has a right-handed neutrino in each 'generation'. Furthermore, we show that the demands can be met upon extending the SM with a copy of the representation 2 ⊗ 1 o , but this has consequences for the number of particle generations.We finally prove that the Minimal Supersymmetric Standard Model is not among the models that satisfy our constraints, but we pose a solution that is a slight extension of the MSSM.

show abstract

“…The matrix algebra of the spectral triple is A = M 3 (C) ⊕ M 2 (C) ⊕ C 8 ∋ (a, b, c, d, e, f, g, h, i, j) and its representation can be read off the Krajewski diagram in figure 3. The model is constructed from diagram 3 in [JS09] and diagram 5 in [JS08]. These diagrams cover for the Standard Model particles, save the right-handed neutrinos, and the X-particles.…”

Section: B Krajewski Diagrams Representations and Fluctuationsmentioning

confidence: 99%

A Dark Sector Extension of the Almost-Commutative Standard Model

Stephan

2014

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

We consider an extension of the Standard Model within the frame work of Noncommutative Geometry. The model is based on an older model [St09] which extends the Standard Model by new fermions, a new U (1)-gauge group and, crucially, a new scalar field which couples to the Higgs field. This new scalar field allows to lower the mass of the Higgs mass from ∼ 170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120 − 130 GeV. The short-coming of the previous model lay in its inability to meet all the constraints on the gauge couplings implied by the Spectral Action. These shortcomings are cured in the present model which also features a "dark sector" containing fermions and scalar particles.

show abstract

On a classification of irreducible almost-commutative geometries V

Cited by 10 publications

References 37 publications

Massive neutrinos in almost-commutative geometry

Massive neutrinos in almost-commutative geometry

Going beyond the Standard Model with noncommutative geometry

A Dark Sector Extension of the Almost-Commutative Standard Model

Contact Info

Product

Resources

About