Advances in Applied Clifford Algebras

, Volume 18, Issue 3–4, pp 621–645 | Cite as

Geometric Tri-Product of the Spin Domain and Clifford Algebras

  • Yaakov Friedman


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 spin 1/2 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.


Spin triple product Spin domain Geometric product Lorentz group representations 


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Copyright information

© Birkhauser 2008

Authors and Affiliations

  1. 1.Department of Applied MathematicsJerusalem College of TechnologyJerusalemIsrael

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