Date: 19 Jul 2005

Octonionic structures in particle physics

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Octonionic extensions of Quantum Mechanics associated with finite exceptional Hilbert spaces are summarized. An interpretation of such spaces as the finite space of internal symmetries allows the introduction of color and flavor degrees of free dom for fundamental particles, color arising from the automorphism group of octonions. As an example the space admitting E symmetry is discussed. The projection operators for various fermion states are constructed and shown to belong to a larger ternary algebra of hermitian operators. A possible application is to the grand unified gauge theory of leptons and quarks based on E6. Another possibility involves the construction of an exceptional superspace by means of octonionic Grassman numbers.