Idea and application of spectrum-generating SU(3) and SU(4)

  • A. Bohm
  • R. B. Teese
Spectrum Generating Groups
Part of the Lecture Notes in Physics book series (LNP, volume 94)


We review the basic ideas of the spectrum-generating SU(n) approach in particle physics, and show the analogy between this and the spectrum-generating method in atomic and molecular physics. We outline the tests of this framework involving one hadron processes and discuss two tests of a fundamental relation of this framework (the Werle relation).


Mass Operator Reduce Matrix Element Cabibbo Angle Hadronic Current Weight Diagram 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. P. Wigner, Nachr. Ges. Wiss. Gött., Math-Phys. Klasse (1932), p. 546. Reprinted in “Group Theory and Solid State Physic-5,” Vol. I, P. H. Meijer, Editor (Gordon and Breach, New York, 1964), pp. 265-278. V. Bargmann, Annals of Math. 59, 1 (1954). G. Ludwig, Grundlagen der Quantum Mechanik (Springer, 1954), p. 101.Google Scholar
  2. 2.
    A. O. Barut and A. Bohm, Phys. Rev. 139B, 1107 (1965).Google Scholar
  3. 3.
    Y. Dothan, M. Gull-Mann and Y. Ne'eman, Phys. Rev. Lett. 17, 145 (1965).Google Scholar
  4. 4.
    N. Mukunda, L. O'Raifeartaigh, and E.C.G. Sudarshan, Phys. Rev. Lett. 15, 1041 (1965).Google Scholar
  5. 5.
    A. Bohm, “Quantum Mechanics,” Chap. II (Springer, New York, 1979).Google Scholar
  6. 6.
    This relation has been suggested in 1965 by J. Werle, “On a symmetry scheme described by a non-Lie algebra,” ICPT preprint, Trieste, 1965, unpublished. It has been incorporated in the spectrum-generating group approach for the mass and spin spectrum, A. Bohm, Phys. Rev. 175, 1767 (1968). Its application in connection with SU(3) has been developer-through the following series of papers: A. Bohm, Phys. Rev. 158, 1408 (1967), Phys. Rev. D7, 2701 (1973); A. Bohm, E.G.C. Sudarshan, Phys. Rev. 178, 2264 (1969). The present scheme has been formulated in reference 7; A. Bohm, J. Werle, Nucl. Phys. B106, 165 (1976). As “dynamical stability group of Pμ/M“ the same idea has also Been arrived at by van Dam and Biedenharn (ref. 9).Google Scholar
  7. 7.
    A. Bohm, Phys. Rev. D13, 2110 (1976).Google Scholar
  8. 8.
    The existence of a theoretical permissibility of a correction factor depending upon the masses, at least for the electromagnetic interaction, has been noted several times before: M. Gourdin, in Symmetries and Quark Models, edited by R. Chand (Gordon and Breach, New York, 1970); R. P. Feynman, Photon Hadron Interaction (Benjamin, New York, 1972); the Duffin-Kummer-Petian formalism: B. G. Kenney, D. C. Peaslee and M. M. Nieto, Phys. Rev. D13, 757 (1976) (see also the talk by Nieto in these Proceedings) for electromagnetic interaction in E. Fischbach, M. M. Nieto, M. Primakoff, C. K. Scott and Smith, Phys. Rev. Lett. 27, 1403 (1971) for Kl 3 decay; another way of describing symmetry-breaking effects by mass dependent correction factors in the effective coupling constant has been suggested by J. Schwinger in Proceedings of the 7th Hawaii Topical Conference on Particle Physics 1977, see also L. F. Urrutia, UCLA preprint (1977).Google Scholar
  9. 9.
    H. van Dam and L. C.Biedenharn, Phys. Rev. D14, 405 (1976).Google Scholar
  10. 10.
    P. Kielanowski (these Proceedings).Google Scholar
  11. 11.
    D. R. Yennie, Phys. Rev. Lett. 34, 239 (1975).Google Scholar
  12. 12.
    A. Bohm and R. B. Teese, Univ. of Texas preprint ORO 317 (to appear in Phys. Rev. D).Google Scholar
  13. 13.
    A. Bohm and R. B. Teese, Phys. Rev. Lett. 38, 629 (1977) and references therein. See also ref. (12).Google Scholar
  14. 14.
    R. Settles, private communication.Google Scholar
  15. 15.
    A. Bohm, Univ. of Texas preprint ORO 316 (to appear in Phys. Rev. D).Google Scholar
  16. 16.
    A. Garcia (these Proceedings).Google Scholar
  17. 17.
    The original suggestion comes, of course, from the nearness of m /mK to the value or tan.Google Scholar
  18. 18.
    This does not mean that the Cabibbo angle cannot be derived from other hypotheses. For example, there have recently been suggestions that tan could be derived in terms of quark mass parameters. H. Fritzsch Phys. Lett. 70B, 436 (1977), A. Ebrahim Phys. Lett. 72B, 457, (1978), H. Terazawa Univ. of Tokyo preprint.Google Scholar
  19. 19.
    M. M. Nieto (these Proceedings).Google Scholar
  20. 20.
    M. Ross, Phys. Letters 36B, 130 (1971).Google Scholar
  21. 21.
    A. Bohm, M. Igarashi, and J. Werle, Phys. Rev. D15, 2461 (1977).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • A. Bohm
    • 1
  • R. B. Teese
    • 2
  1. 1.Center for Particle TheoryUniversity of TexasAustin
  2. 2.Max-Planck Institute für Physik8 München 40Germany

Personalised recommendations