Baryon current solving SU(3) charge-current algebra (original) (raw)

References and Footnotes

1. See the lecture by Barut, A. O.: Springer Tracts in Mod. Phys., Vol. 50 (1969).
   Google Scholar
2. Kleinert, H.: Fortschr. Phys. 16, 1 (1968).
   Article Google Scholar
3. For an extensive study of this subject see: Hamprecht, B., and H. Kleinert: Univ. of Colorado preprint, May 1968; Hamprecht, B.: Fortschr. Phys. 16, 35 (1969). There are very few parameters in this approach reproducing the decay properties of almost the complete Rosenfeld table for baryon resonances.
   Google Scholar
4. Kleinert, H.: Phys. Rev. 163, 1807 (1967). Kleinert, H., Barut, A. O., D. Corrigan, and H. Kleinert: Phys. Rev. Letters 20, 167 (1968). Kleinert, H. Corrigan, D.: University of Colorado, Thesis (1968). In particular, the theory is able to reproduce the experimentally observed double pole formula for G P E =G P M /μ _P_=G n M /μ n and \(G_E^n = \frac{t}{{4m^2 }}G_M^n \).
   Article ADS Google Scholar
5. -: Phys. Rev. Letters 18, 1027 (1967). One simply assumes the pseudoscalar to transform as an octet operator under SU (3) and uses experimental masses. The mass splitting cause SU (3) breaking in the form factors. Only the unphysical transitions at rest are SU (3) symmetric.
   Article ADS Google Scholar
6. Hamprecht, B., and H. Kleinert: Phys. Rev. (in press).
   Google Scholar
7. For simplicity we shall assume isospin invariance of the theory. The electromagnetic breaking effects could be included in this theory in quite the same way as the effect of the medium strong interactions on the strangeness changing currents which we shall focus our attention on. The strangeness changing currents will clearly not be conserved.
   Google Scholar
8. See the other lectures or, for example; Renner, B.: Current algebras, and their applications. Oxford: Pergamon Press 1968.
   MATH Google Scholar
9. Rosenfeld, A. H., et al.: Rev. Mod. Phys. 40, 77 (1968). For some more questionable resonances see Donnachie, A, R. G. Kirsopp, and C. Lovelace Phys. Letters 26 B, 161 (1968).
   Article ADS Google Scholar
10. Kleinert, H.: Phys. Rev. 168 1827 (1968), and Lectures in Theoretical Physics New York: Gordon and Breach 1968.
    Article ADS Google Scholar
11. Barut, A. O., D. Corrigan, and H. Kleinert: Phys. Rev. 167, 1527 (1968).
    Article ADS Google Scholar
12. We absorb the labels s, s 3 in n to simplify the notation.
    Google Scholar
13. Such a wave equation is given by model 5 of Nambu, Y.: Phys. Rev. 160, 1171 (1967).
    Article ADS Google Scholar
14. Grodsky, I. T., and R. F. Streater: Phys. Rev. Letters 20 695 (1968).
    Article ADS Google Scholar
15. We assume the quaternion representation to be given by L=σ/2 and M=_i_σ/2 of the Lorentz group.
    Google Scholar
16. Bebie, H., and H. Leutwyler: Phys. Rev. Letters 19, 618 (1967).
    Article ADS Google Scholar
17. Gell-Mann, M., D. Horn, and J. Weyers: Heidelberg Conference on High Energy Physics and Elementary Particles 1967. Gell-Mann, Leutwyler, H.: University Bern Preprint 1967. Gell-Mann, Kleinert, H.: Montana State University Preprint 1967.
    Google Scholar
18. Cutkosky, R. E., and M. Leon: Phys. Rev. 135, B 1445 (1964).
    Article ADS Google Scholar
19. We use the notation and phase conventions of de Swart, J. J.: Rev. Mod. Phys. 35, 916 (1963). The Racah coefficients are tabulated in Krammer, M.: Acta Phys. Austr., Suppl. 1, 183 (1964). The subscripts β, γ of ν are degeneracy labels.
    Article ADS Google Scholar
20. In (35) we have absorbed the degeneracy labels γ, γ′, in ν′ to simplify the notation. The summation clearly extends over those labels as well.
    Google Scholar
21. Cook, T., C. J. Goebel and B. Sakita: Phys. Rev. Letters 15, 35 (1965).
    Article ADS MathSciNet Google Scholar
22. Kuriyan, J. G., and E. C. G. Sudarshan: Phys. Letters, 21, 106 (1966).
    Article ADS Google Scholar
23. Fulco, J., and D. Y. Wong: Phys. Rev. Letters 15, 274 (1965). The extended bootstrap condition is Γ=C ssu Γ+C st Γ′. For a, detailed discussion of this connection see Fairlie, D. B.: Phys. Rev. 155, 1694 (1968).
    Article ADS MathSciNet Google Scholar
24. Bincer, A. M.: Phys. Rev. 155, 1699 (1967).
    Article ADS Google Scholar
25. For a review on the status of SU (3) and further references see D. D. Reeders talk at the Argonne Symposium 1967.
    Google Scholar
26. Kernan, A., and W. M. Smart: Phys. Rev. Letters 17, 832 (1966).
    Article ADS Google Scholar
27. Goldberg, M. et al.: Nuovo Cimento 45, 169 (1966), and Tripp, R., et al.: UCRL Report No. 17385 (unpublished).
    Article ADS Google Scholar
28. Barut, A. O., and H. Kleinert: Phys. Rev. Letters 18, 754 (1967).
    Article ADS Google Scholar
29. For a review of this subject see Kleiner, H.: In: Lectures in Theoretical Physics, Vol. 10. New York: Gordon and Breach 1968.
    Google Scholar
30. Corrigan, D., B. Hamprecht, and H. Kleinert: Nuclear Physics B (in press).
    Google Scholar
31. Nambu, Y.: Progr. Theor Phys., Commemorative issue in honour of S. Tomonaga, 1966.
    Google Scholar
32. Bjorken, J. D., and J. D. Walecka: Ann. Phys. 38, 35 (1966).
    Article ADS Google Scholar
33. Reviews on nucleon form factors are contained in W. K. H. Panofsky, Rapporteur's Talk at the Heidelberg International Conference on Elementary Particles, September 1967; H. Joos, ibid. Talk at the Heidelberg International Conference on Elementary Particles, September 1967, Hand, L. H.: Proc. of Inter. Conf. on Particles and Fields. New York: Interscience 1967.
    Google Scholar
34. Recent measurement of nucleon form factors at CEA: Gotein, M., et al.: Phys. Rev. Letters 18, 106 (1967).—DESY: Albrech, W., et al.: Phys. Rev. Letters 18, 1014 (1967); and SLAC: R. Taylor.—Paper delivered at the International Symposium on Electron and Photon Interactions at high Energies, SLAC, September, 1967.
    Google Scholar
35. Dunning, J. R., et al.: Phys. Rev. 141, 1286 (1966).
    Article ADS Google Scholar
36. Walecka J. D., and P. A. Zucker: Phys. Rev. 167, 1479 (1968).
    Article ADS Google Scholar
37. Cone, A. A., et al.: Phys. Rev. 156, 1490 (1967).
    Article ADS Google Scholar
38. Lynch, H. L., et al.: HEPL-494 B (1967).
    Google Scholar
39. Brasse, F., et al.: DESY preprint 67/34, 1967;—Ash, W. W., et al.: Phys. Letters 24 B, 165 (1967);—Tsai, Y. S.: SLAC-PUB-364 (Nov. 1967).
    Google Scholar
40. Dalitz, R. H., and D. G. Sutherland: Phys. Rev. 146, 1180 (1966).
    Article ADS Google Scholar

Download references