Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra

@article{Furey2018ThreeGT,
  title={Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra},
  author={C. Furey},
  journal={Physics Letters B},
  year={2018}
}
  • C. Furey
  • Published 1 October 2018
  • Physics, Mathematics
  • Physics Letters B
Abstract A considerable amount of the standard model's three-generation structure can be realised from just the 8 C -dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64 C -dimensional space. Here we identify an s u ( 3 ) ⊕ u ( 1 ) action which splits this 64 C -dimensional space into complexified generators of S U ( 3 ) , together with 48 states. These 48 states exhibit the behaviour of exactly three… Expand

Figures from this paper

On Jordan-Clifford Algebras, Three Fermion Generations with Higgs Fields and a SU(3)× SU(2)L × SU(2)R × U(1) model
It is shown how the algebra J3[C⊗O]⊗Cl(4,C) based on the tensor product of the complex Exceptional Jordan J3[C⊗O], and the complex Clifford algebra Cl(4,C), can describe all of the spinorial degreesExpand
Braided fermions from Hurwitz algebras
  • N. Gresnigt
  • Physics
  • Journal of Physics: Conference Series
  • 2019
Some curious structural similarities between a recent braid- and Hurwitz algebraic description of the unbroken internal symmetries for a single generations of Standard Model fermions were recentlyExpand
Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
We provide theoretical evidence that the neutrino is a Majorana fermion. This evidence comes from assuming that the standard model and beyond-standard-model physics can be described through divisionExpand
S U ( 3 ) C × S U ( 2 ) L × U ( 1 ) Y × U ( 1 ) X as a symmetry of division algebraic ladder operators.
  • C. Furey
  • Physics, Medicine
  • The European physical journal. C, Particles and fields
  • 2018
TLDR
This paper shows how ladder operators arise from the division algebras R, C, H, and O, and from the SU(n) symmetry of these ladder operators, a model which has much structural similarity to Georgi and Glashow's SU(5) grand unified theory is demonstrated. Expand
On the Problem of Choosing Subgroups of Clifford Algebras for Applications in Fundamental Physics
  • Robert Arnott Wilson
  • Advances in Applied Clifford Algebras
  • 2021
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. An algebraist’s perspective on the many subgroups andExpand
Left-Right symmetric fermions and sterile neutrinos from complex split biquaternions and bioctonions
In this article we investigate the application of complex split biquaternions and bioctonions to the standard model. We show that the Clifford algebras Cl(3) and Cl(7) can be used for makingExpand
The $C\ell(8)$ algebra of three fermion generations with spin and full internal symmetries
In this paper, the basis states of the minimal left ideals of the complex Clifford algebra $C\ell(8)$ are shown to contain three generations of Standard Model fermion states, with full Lorentzian,Expand
The Characteristic Equation of the Exceptional Jordan Algebra: Its Eigenvalues, and Their Possible Connection with the Mass Ratios of Quarks and Leptons
The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional LieExpand
The case for a natural composite boson and negative vacuum energy
We revisit a dynamical symmetry breaking model with 4-fermion interactions. A prescription is proposed to remove the momentum routing ambiguity associated with fermion-antifermion condensations. TheExpand
The case for a natural composite boson and negative vacuum energy
We revisit a dynamical symmetry breaking model with 4-fermion interactions. A prescription is proposed to remove the momentum routing ambiguity associated with fermion-antifermion condensations. TheExpand
...
1
2
3
...

References

SHOWING 1-10 OF 59 REFERENCES
Standard Model Fermions and N=8 supergravity
In a scheme originally proposed by M. Gell-Mann, and subsequently shown to be realized at the SU(3)xU(1) stationary point of maximal gauged SO(8) supergravity by N. Warner and one of the presentExpand
Charge quantization from a number operator
Abstract We explain how an unexpected algebraic structure, the division algebras, can be seen to underlie a generation of quarks and leptons. From this new vantage point, electrons and quarks areExpand
Generations: three prints, in colour
A bstractWe point out a somewhat mysterious appearance of SUc(3) representations, which exhibit the behaviour of three full generations of standard model particles. These representations are found inExpand
Gauged Discrete Symmetries and Proton Stability
Author(s): Mohapatra, Rabindra N; Ratz, Michael | Abstract: We discuss the results of a search for anomaly-free Abelian ZN discrete symmetries that lead to automatic R-parity conservation and preventExpand
Nonanomalous discrete R symmetry decrees three generations.
We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R symmetry larger than R parity, provided that the supersymmetric standard model can beExpand
Yang-Mills Interactions and Gravity in Terms of Clifford Algebra
A model of Yang-Mills interactions and gravity in terms of the Clifford algebra Cℓ0,6 is presented. The gravity and Yang-Mills actions are formulated as different order terms in a generalized action.Expand
Three-family particle physics models from global F-theory compactifications
A bstractWe construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the MinimalExpand
The Algebra of Grand Unified Theories
The Standard Model is the best tested and most widely accepted theory of elementary particles we have today. It may seem complicated and arbitrary, but it has hidden patterns that are revealed by theExpand
Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs
We analyze constraints for embedding local SU(5) F-theory GUTs into consistent compactifications and construct explicit three-generation models based on the geometry of [1]. The key tool for studyingExpand
Octonions, E6, and particle physics
In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be describedExpand
...
1
2
3
4
5
...