Octonionic structures in particle physics

  • Feza Gürsey
Group Theory in Particle Physics
Part of the Lecture Notes in Physics book series (LNP, volume 94)


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.


Gauge Boson Jordan Algebra Projective Geometry Grand Unify Theory Colored State 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Feza Gürsey
    • 1
  1. 1.Yale UniversityNew Haven

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