Yang-Mills Interactions and Gravity in Terms of Clifford Algebra

Details Yang-Mills Interactions and Gravity in Terms of Clifford Algebra Yang-Mills Interactions and Gravity in Terms of Clifford Algebra

2010-07-31

arxiv.org/abs/1008.0122v1

Adv.Appl.Clifford Algebras 21:145-163,2011

Physics

General Physics

20 pages, to appear in Advances in Applied Clifford Algebras

Scientific paper

10.1007/s00006-010-0243-7

A model of Yang-Mills interactions and gravity in terms of the Clifford algebra Cl(0,6) is presented. The gravity and Yang-Mills actions are formulated as different order terms in a generalized action. The feebleness of gravity as well as the smallness of the cosmological constant and theta terms are discussed at the classical level. The invariance groups, including the de Sitter and the Pati-Salam SU(4) subgroups, consist of gauge transformations from either side of an algebraic spinor. Upon symmetry breaking via the Higgs fields, the remaining symmetries are the Lorentz SO(1,3), color SU(3), electromagnetic U(1)_EM, and an additional U(1). The first generation leptons and quarks are identified with even and odd parts of spinor idempotent projections. There are still several shortcomings with the current model. Further research is needed to fully recover the standard model results.

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