Exceptional quantum geometry and particle physics

DOI10.1016/j.nuclphysb.2016.04.018zbMath1349.81179arXiv1604.01247OpenAlexW2336907355MaRDI QIDQ341869

Michel Dubois-Violette

Publication date: 17 November 2016

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.01247

Mathematics Subject Classification ID

Unified quantum theories (81V22) Exceptional Jordan structures (17C40) Strong interaction, including quantum chromodynamics (81V05) Weak interaction in quantum theory (81V15) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (18)

Superconnection in the spin factor approach to particle physics ⋮ Particle models from special Jordan backgrounds and spectral triples ⋮ Spin(11, 3), particles, and octonions ⋮ Dynamics of fluctuations and spinodal decomposition in polymer blends ⋮ Leptons, quarks, and gauge from the complex Clifford algebra \(\mathbb {C}\ell _6\) ⋮ Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra ⋮ Left-right symmetric fermions and sterile neutrinos from complex split biquaternions and bioctonions ⋮ Octonionic Clifford algebra for the internal space of the standard model ⋮ The conformal-symmetry-color-neutrality connection in strong interaction ⋮ Exceptional quantum geometry and particle physics. II ⋮ The geometry of physical observables ⋮ Differential calculus on Jordan algebras and Jordan modules ⋮ Color confinement at the boundary of the conformally compactified \(\mathrm{AdS}_5\) ⋮ Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra ⋮ Octonions, exceptional Jordan algebra and the role of the group \(F_4\) in particle physics ⋮ On Jordan-Clifford algebras, three fermion generations with Higgs fields and a \(\mathrm{SU}(3) \times \mathrm{SU}(2)_L \times \mathrm{SU}(2)_R \times \mathrm{U}(1)\) model ⋮ SO(9) characterization of the standard model gauge group ⋮ Jordan algebraic interpretation of maximal parabolic subalgebras: exceptional Lie algebras

Cites Work

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• Prime Jordan algebras. II
• Prime Jordan algebras
• Moufang plane and octonionic quantum mechanics
• \(SU(n)\)-connections and noncommutative differential geometry
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• The geometry of Jordan and Lie structures
• Differential calculus on compact matrix pseudogroups (quantum groups)
• On the first-order operators in bimodules
• Gravity and the standard model with neutrino mixing
• Non-associative geometry and the spectral action principle
• Exceptional gauge groups and quantum theory
• Non-commutative geometry, non-associative geometry and the standard model of particle physics
• Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry
• Lorentzian version of the noncommutative geometry of the standard model of particle physics
• Noncommutative differential geometry and new models of gauge theory
• Classical bosons in a non-commutative geometry
• Quark structure and octonions
• Classification of simple z-graded lie superalgebras and simple jordan superalgebras
• The octonions
• Representation theory of Jordan superalgebras I
• A Theory of Power-Associative Commutative Algebras
• Particle models and noncommutative geometry
• Introduction to \(A\)-infinity algebras and modules
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