Geometric tri-product of the spin domain and Clifford algebras

Details Geometric tri-product of the spin domain and Clifford algebras Geometric tri-product of the spin domain and Clifford algebras

2005-10-02

arxiv.org/abs/math-ph/0510008v1

Advances in Applied Clifford Algebras, Birkhauser, (2008) 621-645

Physics

Mathematical Physics

28 pages, 4 figures

Scientific paper

We show that the triple product defined by the spin domain (Bounded Symmetric Domain of type 4 in Cartan's classification) is closely related to the geometric product in Clifford algebras. We present the properties of this tri-product and compare it with the geometric product. The spin domain can be used to construct a model in which spin 1 and spin1/2 particles coexist. Using the geometric tri-product, we develop the geometry of this domain. We present a geometric spectral theorem for this domain and obtain both spin 1 and spin 1/2 representations of the Lorentz group on this domain.

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