De Sitter Fibers and SO(3,2) Spectrum Generating Group for Hadrons


In order to convince you of the relevance of my topic for an Einstein Centennial celebration let me start with a quote.1


Gauge Group Fiber Bundle Minkowski Space Base Space Relativistic Rotator 
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  1. 1.
    A. Bohm, Lectures in Theoretical Physics, Boulder Lectures (1966), Vol. 9B, p. 327, Gordon and Breach, A. O. Barut, editor. The idea to picture hadrons as micro-de Sitter spaces of infinite time and finite space extension was suggested in A. O. Barut and A. Bohm, Phys, Rev. 139, B1107 (1965); A. Bohm, Phys. Rev. 145 1212 (1966). The general idea that the “dynamics” of hadrons leads to a “dynamical symmetry group,” which is larger than the space-time symmetry group, has been proposed earlier, see A. O. Barut, Phys. Rev. 135 B839 (1964). de Sitter momentum spaces have been introduced by A. D. Donkov, V. G. Kadyshevsky, M. D. Mateev, and R. M. Mir-Kasimov, Bulgar. Journ. of Physics 1, 58, 150, 233 (1974); 2, 3 (1975); see also V. G. Kadyshevsky, p. 114, in Group Theoretical Methods in Physics, Lecture Notes in Physics, Vol. 94, Springer-Verlag, New York (1979). That this (4+1) de Sitter group be a gauge group of strong interaction was suggested by W. Drechsler using Cartan type fiber bundles in Ref. 2.Google Scholar
  2. 2.
    W. Drechsler, Fortschritte der Physik 23, 607 (1975).MathSciNetADSCrossRefGoogle Scholar
  3. W. Drechsler, Found. Phys. 7, 629 (1977).MathSciNetADSCrossRefGoogle Scholar
  4. W. Drechsler, “Gauge Theory of Strong and Electromagnetic Interactions Formulated on a Fiber Bundle of Cartan Type,” Texas Lectures, Springer Lecture Notes in Physics, Volume 67 (1977).Google Scholar
  5. 3.
    E. Cartan, Ann. E. Norm. 40, 325 (1922); 41, 1 (1924); Bull. Sc. Math. 48, 294 (1924). For the general definition of a solder form see S. Kobayashi, Can. J. Math. 8, 145 (1956). For a comparison of Cartan’s viewpoint with the conventional approach to connections, see Comment 5 of S. S.ernberg in Differential Geometrical Methods in Mathematical Physics II, K. Bleuler et al., editors, p. 2, Springer Verlag, 1978.Google Scholar
  6. 4.
    This is called the unitary gauge choice in K. S. Stelle and P. C. West, Imperical College London preprint ICTP/7879/19.Google Scholar
  7. 5.
    H. van Dam, L. C. Biedenharn, Phys. Rev. D14, 405 (1976); Physics Letters 62B, 190 (1976).Google Scholar
  8. 6.
    A. Bohm, Phys. Rev. 175, 1767 (1968). This was based upon an idea by P. Budini and C. Fronsdal, Phys. Rev. Lett. 14, 968 (1965);Google Scholar
  9. V. Ottoson, A. Kihlberg, J. S. Nilsson, Phys. Rev. 137, B658 (1965).MathSciNetADSCrossRefGoogle Scholar
  10. 7.
    P. A. M. Dirac, J. Math. Phys. 4, 901 (1963).MathSciNetADSMATHCrossRefGoogle Scholar
  11. E. Majorana, Nuovo Cimento 9, 335 (1932).MATHCrossRefGoogle Scholar
  12. 8a).
    E. Inönü, E. P. Wigner, Proc. N.A.S. 39, 50 (1953);Google Scholar
  13. b).
    A. Bohm, “The Connection Between Representations of SO (4, 1) and the Poincaré Group,” p. 197, Studies in Mathematical Physics, A. O. Barut, ed. (1973);Google Scholar
  14. c).
    W. Drechsler, J. Math. Phys. 18, 1358 (1976).MathSciNetADSCrossRefGoogle Scholar
  15. 9.
    F. Rohrlich, Nucl. Phys. B112, 177 (1978);MathSciNetADSCrossRefGoogle Scholar
  16. L. P. Staunton, Phys. Rev. D13, 3269 (1976);MathSciNetADSGoogle Scholar
  17. H. Bacry, J. Math. Phys. 5, 109 (1964);MathSciNetADSMATHCrossRefGoogle Scholar
  18. R. J. Finkelstein, Phys. Rev. 75, 1079 (1949);MathSciNetADSMATHCrossRefGoogle Scholar
  19. H. S. Snyder, Phys. Rev. 71, 38 (1947).ADSMATHCrossRefGoogle Scholar
  20. 10.
    F. Gürsey, Group Theoretical Concepts and Methods in Elementary Particle Physics (1964), p. 365.Google Scholar
  21. C. Fronsdal, Rev. Mod. Phys. 37, 221 (1965).MathSciNetADSCrossRefGoogle Scholar
  22. 11.
    Gauge groups whose structure constants change over space-time, A. N. Lesnov, V. I. Manko, Lebedev Inst. preprint No. 22, Moscow, 1978 and “bundles” with fibers of different curvatures are generalizations of the conventional differential geometrical concepts whose mathematical foundations have not yet been worked out.Google Scholar
  23. 12.
    L. Jaffe, J. Math. Phys. 12, 882 (1971).MathSciNetADSCrossRefGoogle Scholar
  24. 13.
    E. P. Wigner, Unitary Representations of the Inhomogeneous Lorentz Group Including Reflections, Istanbul Lectures (1964). F. Gürsey, ed.Google Scholar
  25. 14a).
    T. E. Kalogeropoulos, G. S. Tzanakos, Proc. of 3rd European Symposium on NN interactions, Stockholm (1976), and private communication;Google Scholar
  26. b).
    L. Montanet, Proc. of XIII Rencontres de Moriond, Flaine, France (1978), CERN(EP) Phys. 77–22 (1977);Google Scholar
  27. c).
    R. S. Dulude et al., IV International Antiproton Symposium, Strasbourg ( 1978 ), Physics Letters, June 1978;Google Scholar
  28. d).
    A. A. Carter et al., Phys. Letters 67B, 117 (1977);ADSCrossRefGoogle Scholar
  29. e).
    e) A. Apostolakis et al., Phys. Letters 66B, 185 (1977);ADSCrossRefGoogle Scholar
  30. f).
    f) C. Evangelista et al., Phys. Letters 72B, 139 (1977);ADSCrossRefGoogle Scholar
  31. g).
    g) A. A. Carter, unpublished, May 1978;Google Scholar
  32. h).
    A. Carter, Rutherford Laboratory Preprint RL/78/032 (1978);Google Scholar
  33. i).
    R. Baldi et al., Phys. Lett. 74B, 413 (1978).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • A. Bohm
    • 1
  1. 1.Physics DepartmentThe University of Texas at AustinAustinUSA

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