Octonionic Cl(6) flavor structure yields φ12 = -2χ for quarks and real lepton amplitudes unless identity-flavor plane mixing occurs.
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abstract
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.
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Introduces a canonical Clifford-split-octonion framework to construct massless ladder representations of U(2,2) and restrict them to Sp(2,2) with explicit invariant forms and operators.
Using Hermitian elements of J3(OC) and cubic ladders for mass ratios as inputs, the paper constructs an effective bridge ansatz for two-generation mixing, deriving the local phase law φ12=-2χ in the quark sector with a fitted effective Cabibbo phase of ~105.7°.
Phenomenological deformation of an exceptional-Jordan framework that fits hierarchy exponent and normalizations to six charged-fermion mass ratios at MZ, yielding power-law relations while accommodating neutrino orderings.
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Massless Representations in Conformal Space and Their de Sitter Restrictions
Introduces a canonical Clifford-split-octonion framework to construct massless ladder representations of U(2,2) and restrict them to Sp(2,2) with explicit invariant forms and operators.