Group Theoretical Methods in Physics pp 301-310 | Cite as

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

Spectrum Generating Groups

First Online:

## Abstract

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).

## Keywords

Mass Operator Reduce Matrix Element Cabibbo Angle Hadronic Current Weight Diagram## Preview

Unable to display preview. Download preview PDF.

## References

- 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.A. O. Barut and A. Bohm, Phys. Rev. 139B, 1107 (1965).Google Scholar
- 3.Y. Dothan, M. Gull-Mann and Y. Ne'eman, Phys. Rev. Lett. 17, 145 (1965).Google Scholar
- 4.N. Mukunda, L. O'Raifeartaigh, and E.C.G. Sudarshan, Phys. Rev. Lett. 15, 1041 (1965).Google Scholar
- 5.A. Bohm, “Quantum Mechanics,” Chap. II (Springer, New York, 1979).Google Scholar
- 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suggested in 1965 by J. Werle, “On a symmetry scheme described by a non-Lie algebra,” ICPT preprint, Trieste, 1965, unpublished.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 P
_{μ}/M“ the same idea has also Been arrived at by van Dam and Biedenharn (ref. 9).Google Scholar - 7.A. Bohm, Phys. Rev. D13, 2110 (1976).Google Scholar
- 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 K
_{l}_{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.H. van Dam and L. C.Biedenharn, Phys. Rev. D14, 405 (1976).Google Scholar
- 10.P. Kielanowski (these Proceedings).Google Scholar
- 11.D. R. Yennie, Phys. Rev. Lett. 34, 239 (1975).Google Scholar
- 12.A. Bohm and R. B. Teese, Univ. of Texas preprint ORO 317 (to appear in Phys. Rev. D).Google Scholar
- 13.A. Bohm and R. B. Teese, Phys. Rev. Lett. 38, 629 (1977) and references therein. See also ref. (12).Google Scholar
- 14.R. Settles, private communication.Google Scholar
- 15.A. Bohm, Univ. of Texas preprint ORO 316 (to appear in Phys. Rev. D).Google Scholar
- 16.A. Garcia (these Proceedings).Google Scholar
- 17.The original suggestion comes, of course, from the nearness of m /m
_{K}to the value or tan.Google Scholar - 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.M. M. Nieto (these Proceedings).Google Scholar
- 20.M. Ross, Phys. Letters 36B, 130 (1971).Google Scholar
- 21.A. Bohm, M. Igarashi, and J. Werle, Phys. Rev. D15, 2461 (1977).Google Scholar

## Copyright information

© Springer-Verlag 1979