A Geometric Approach to the Standard Model

Abstract

A geometric approach to the standard model in terms of the Clifford algebra is advanced. The gauge symmetries and charge assignments of the fundamental fermions are seen to arise from a simple geometric model involving extra space-like dimensions. The bare coupling constants are found to obey $g_s/g=1$ and $g^{\prime }/g=\sqrt{3/5}$, consistent with SU(5) grand unification but without invoking the notion of master groups. In constructing the Lagrangian density terms, it is found that the Higgs isodoublet field emerges in a natural manner. A matrix representation of is included as a computational aid.

14 pages, 4 tables

Cited by in corpus (9)

• An Exceptionally Simple Theory of Everything
• The Standard Model Algebra - Leptons, Quarks, and Gauge from the Complex Clifford Algebra Cl6
• Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
• Left-Right symmetric fermions and sterile neutrinos from complex split biquaternions and bioctonions
• Yang-Mills Interactions and Gravity in Terms of Clifford Algebra
• Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone Bosons
• Clifford bundle formulation of BF gravity generalized to the standard model
• Chiral asymmetry in the weak interaction via Clifford Algebras
• Quantum number conservation: a tool in the design and analysis of high energy experiments