Octonionic structures in particle physics

  • Feza Gürsey
Group Theory in Particle Physics

DOI: 10.1007/3-540-09238-2_117

Part of the Lecture Notes in Physics book series (LNP, volume 94)
Cite this paper as:
Gürsey F. (1979) Octonionic structures in particle physics. In: Beiglböck W., Böhm A., Takasugi E. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 94. Springer, Berlin, Heidelberg


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.


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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

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

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