Quaternionic quantum mechanics and Adler's chromostatics

  • L. C. Biedenharn
  • D. Sepunaru
  • L. P. Horwitz
Canonical Transformation and Quantum Mechanics
Part of the Lecture Notes in Physics book series (LNP, volume 135)


Gauge Group Tensor Product Gauge Field Quaternion Algebra Tensor Product Space 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I.B. Khriplovich, Sov.Phys.JETP 47,1 (1978)[Zh.Eksp.Teor.Fiz. 74,37 (1978)]Google Scholar
  2. 2.
    R. Giles and L. McLerran, Phys.Lett. 79B,447 (1978);Phys. Rev. D19, 3732(1979);Phys.Rev. D21,1672 (1980).ADSGoogle Scholar
  3. 3.
    S.L. Adler, Phys. Rev. D17,3212 (1978).ADSGoogle Scholar
  4. 4.
    S.L. Adler,Phys. Rev. D18, 411 (1978); Phys.Lett. 86B,203(1979); Phys. Rev. D19,1168(1979;Phys. Rev. D20, 1386(1979.ADSGoogle Scholar
  5. 5.
    S.L. Adler, “Quaternionic Chromodynamics as a Theory of Composite Quarks and Leptons”, Inst. for Adv. Study preprint, December,1979Google Scholar
  6. 6.
    H. Harari, Phys. Lett. 86B, 83 (1979).ADSGoogle Scholar
  7. 7.
    M.A. Shupe, Phys. Lett. 86B, 87 (1979).ADSGoogle Scholar
  8. 8.
    J.E. Mandula, Phys. Rev. D14, 3497 (1976).ADSGoogle Scholar
  9. 9.
    L.C. Biedenharn, J. Math. Phys. 4, 436 (1963).(D-operators for SU(n).)MATHMathSciNetCrossRefADSGoogle Scholar
  10. 10.
    V. Rittenberg and D. Wyler, Phys. Rev.. D18, 4806 (1978).MathSciNetADSGoogle Scholar
  11. 11.
    P. Cvitanovic, R.J. Gonsalves and D.E. Neville, Phys. Rev. D18, 3881 (1978).ADSGoogle Scholar
  12. 12.
    S. C. Lee, Phys. Rev. D20, 1951 (1979).ADSGoogle Scholar
  13. 13.
    L.C. Biedenharn, “Group Theoretical Approaches to Nuclear Spectroscopy”,258-421, in“Lectures in Theoretical Physics”,edited by, W.E. Brittin, B.N. Downs and Joanne Downs, Vol. 5 (Interscience, New York) 1963.Google Scholar
  14. 14.
    L.P. Horwitz, D. Sepunaru, L.C. Biedenharn, “Quaternion Quantum Mechanics and Second Qunatization”(to be submitted to Comm. Math. Phys.)Google Scholar
  15. 15.
    C. Piron, Foundations of Quantum Physics, W.A. Benjamin, Reading Mass. (1976). See also L.P. Horwitz and L.C. Biedenharn, Helv. Phys. Acta, 38, 385 (1965); M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw Hill, New York (1966).MATHGoogle Scholar
  16. 16.
    E.C.G. Stueckelberg, Helv.Phys. Acta 33,727 (1960)MATHMathSciNetGoogle Scholar
  17. 16a.
    E.C.G. Stueckelberg, and M. Guenin, Helv. Phys. Acta 34,621 (1961)MATHGoogle Scholar
  18. 16 b).
    E.C.G. Stueckelberg, C. Piron and H. Ruegg, Helv. Phys Acta 34, 675 (1961)MATHGoogle Scholar
  19. 16 c).
    E.C.G. Stueckelberg and M. Guenin, Helv.Phys.Acta 35, 673 (1962).MATHGoogle Scholar
  20. 17.
    M. Günaydin and F. Gürsey, Lett. Nuovo Cimento 6, 401 (1973);Jour, Math. Phys. 14, 1651 (1973);Phys. Rev. D9, 3387(1974); F. Gursey, in /ldJohns Hopkins University Workshop on Current Problems in High Energy Particle Theory”, Baltimore, Md. (1974); M. Gunaydin, Jour. Math. Phys. 17, 1875 (1976).CrossRefGoogle Scholar
  21. 18.
    H.H. Goldstine and L.P. Horwitz, Math. Ann. 164,291 (1966).MATHMathSciNetCrossRefGoogle Scholar
  22. 19.
    If one has two vector spaces, one quaternion linear on the left and the other quaternion linear on the right, the juxtaposed product is then quaternion linear on both the left and the right. However, this is not an acceptable tensor product since half of the quaternion action on each of the two vector spaces is lost. For more than two vector spaces even a tensor product of this type cannot be defined. We wish to thank Professor Jaques Tits for discussing this subject with us.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • L. C. Biedenharn
    • 1
  • D. Sepunaru
    • 1
  • L. P. Horwitz
    • 2
  1. 1.Physics DepartmentDuke University DurhamNorth CarolinaUSA
  2. 2.Department of Physics and AstronomyTel Aviv UniversityRamat AvivIsrael

Personalised recommendations