Abstract

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into left-sided ("exterior") and right-sided ("interior") types. By definition, Poincare transformations are exterior ones. We consider all rotations in the seven-dimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. These rotations comprise additional exterior transformations that commute with the Poincare group and form the group SU(2)_L, interior ones that constitute SU(3)_C, and a unique group of coupled double-sided rotations with U(1)_Y symmetry. The spinor mediates a physical coupling of Poincare and isotopic symmetries within the restrictions of the Coleman--Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of SU(2). The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.

Publication Date

4-20-2001

Comments

Also archived at: arXiv:hep-th/0103137 v2 26 Mar 2001 This work was supported by the Natural Sciences and Engineering Research Council of Canada.ISSN:1361-6447 Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

School of Physics and Astronomy (COS)

Campus

RIT – Main Campus

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