Foundations of Physics

, Volume 8, Issue 3–4, pp 303–311 | Cite as

Nine-vectors, complex octonion/quaternion hypercomplex numbers, lie groups, and the ‘real’ world

  • James D. EdmondsJr.


A “mental” multiplication scheme is given for the super hypercomplex numbers, which extend the 16-element Dirac algebra to 32 elements by appending the complex octonions. This extends the 5-vectors of relativity to 9-vectors. The problems with nonassociativity, for the group structures and wave equation covariance, are explored.


Covariance Wave Equation Multiplication Scheme Group Structure Equation Covariance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Günaydin and F. Gürsey,J. Math. Phys. 14, 1651 (1973); M. Günaydin,Univ. Bonn Preprint (1976).Google Scholar
  2. 2.
    A. Pais,Phys. Rev. Lett. 7, 29 (1961).Google Scholar
  3. 3.
    R. Penney,Nuovo Cimento 3B, 95 (1971).Google Scholar
  4. 4.
    J. D. Edmonds, Jr.,Found. Phys. 5, 239 (1975), and to be published;Int. J. Theor. Phys. 11, 309 (1974);13, 297 (1975); and to be published;Lett. Nuovo Cim. 13, 185 (1975).Google Scholar
  5. 5.
    J. D. Edmonds, Jr.,Int. J. Theor. Phys. 13, 431 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • James D. EdmondsJr.
    • 1
  1. 1.Department of PhysicsBucknell UniversityLewisburg

Personalised recommendations