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- W3194855467 abstract "A unified theory of elementary fermions is formulated, based on the Standard Model. Seven commuting elements of the Clifford algebra $Cl_{7,7}$ define binary quantum numbers that characterise $2^7 = 128$ states of 32 elementary fermions. This algebra determines all possible fermion interactions, and the Lie algebras of all known gauge fields are sub-algebras. Unit spatial displacements correspond to three generators of the algebra, and unit time intervals correspond to the product of all 14 generators. A $Cl_{3,3}$ sub-algebra describes first generation leptons in terms of three binary quantum numbers that distinguish them as components of a Lorentz invariant 8-spinor. The Dirac equation is reformulated as a Lorentz invariant operator acting on invariant 4-spinors. The Standard Model of electro-weak interactions is reformulated to take account of finite neutrino mass, showing the concept of chirality to be redundant. A $Cl_{5,5}$ sub-algebra describes an internal hadron substrate, which distinguishes quarks and leptons in a way that is consistent with the Standard Model of the strong interaction. The $Cl_{7,7}$ algebra incorporates flavour symmetry and distinguishes the three observed fermion generations. It also predicts a fourth fermion generation, with no neutrino and a distinct substrate, providing a candidate for dark matter. Relationships of the $Cl_{1,3}$ algebra with general relativity, and of $Cl_{5,5}$ sub-algebras with SO(32) string theory are explored." @default.
- W3194855467 created "2021-08-30" @default.
- W3194855467 creator A5012776480 @default.
- W3194855467 date "2021-08-10" @default.
- W3194855467 modified "2023-09-27" @default.
- W3194855467 title "Reformulation and extension of the Standard Model using Clifford algebra" @default.
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