Exceptional quantum geometry and particle physics

@article{DuboisViolette2016ExceptionalQG,
  title={Exceptional quantum geometry and particle physics},
  author={Michel Dubois-Violette},
  journal={Nuclear Physics},
  year={2016},
  volume={912},
  pages={426-449}
}

Exceptional Quantum Algebra for the Standard Model of Particle Physics

  • I. Todorov
  • Physics, Mathematics
    Springer Proceedings in Mathematics & Statistics
  • 2020
The exceptional euclidean Jordan algebra of 3x3 hermitian octonionic matrices, appears to be tailor made for the internal space of the three generations of quarks and leptons. The maximal rank

The Characteristic Equation of the Exceptional Jordan Algebra: Its Eigenvalues, and their relation with the Mass Ratios of Quarks and Leptons

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal

Exceptional quantum geometry and particle physics II

Quantum gravity effects in the infrared: a theoretical derivation of the low-energy fine structure constant and mass ratios of elementary particles

  • T. P. Singh
  • Physics
    The European Physical Journal Plus
  • 2022
We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This theory offers the prospect of unifying internal symmetries of

The Standard Model Algebra - Leptons, Quarks, and Gauge from the Complex Clifford Algebra Cl6

A simple geometric algebra is shown to contain automatically the leptons and quarks of a family of the Standard Model, and the electroweak and color gauge symmetries, without predicting extra

Quantum gravity effects in the infra-red: a theoretical derivation of the low energy fine structure constant and mass ratios of charged fermions

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This theory offers the prospect of unifying internal symmetries of

Color confinement at the boundary of the conformally compactified AdS5

Abstract The topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal boundary of AdS5 spacetime, topologically

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 Lie

A remarkable dynamical symmetry of the Landau problem

We show that the dynamical group of an electron in a constant magnetic feld is the group of symplectomorphisms Sp(4, R). It is generated by the spinorial realization of the conformal algebra so(2,3)

Trace dynamics and division algebras: towards quantum gravity and unification

Abstract We have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade
...

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