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Foundations of Physics

, Volume 23, Issue 5, pp 751–767 | Cite as

Relativistic and nonrelativistic dynamical groups

Part IV. Invited Papers Dedicated To Asim Orhan Barut

Abstract

The physical motivations for the dynamical group are presented and it is shown how Barut's mathematical speculations were combined with the idea of an elementary length to provide group theoretical models of relativistic extended objects. Then the simplest nonrelativistic and relativistic models are described.

Keywords

Theoretical Model Relativistic Model Dynamical Group Elementary Length Extended Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. O. Barut,Phys. Rev. B 135, 839 (1964).Google Scholar
  2. 2.
    W. Heisenberg,Z. Phys. 101, 533 (1936);Z. Phys. 110, 251 (1938).Google Scholar
  3. 3.
    E. P. Wigner,Ann. Math. 40, 199 (1939).Google Scholar
  4. 4.
    W. Pauli,Z. Phys. 36, 336 (1926); V. Fock,Z. Phys. 98, 145 (1935); V. Bargmann,Z. Phys. 99, 576 (1936).Google Scholar
  5. 5.
    J. P. Elliott,Proc. R. Soc. London A 245, 128, 562 (1958).Google Scholar
  6. 6.
    S. Goshen and J. H. Lipkin,Ann. Phys. (Leipzig) 6, 301 (1959).Google Scholar
  7. 7.
    A. O. Barut and A. Bohm,Phys. Rev. B 139, 1107 (1965).Google Scholar
  8. 8.
    Y. Dothan, M. Gell-Mann, and Y. Ne'eman,Phys. Rev. Lett. 17, 148 (1965).Google Scholar
  9. 9.
    W. Heisenberg,Phys. Today 29(3), 32 (1976).Google Scholar
  10. 10.
    A. Bohm, B. Kendrick, M. E. Loewe, and L. J. Boya,J. Math. Phys. 33, 977 (1992); A. Bohm, inClassical and Quantum Systems, Proceedings of the II International Wigner Symposium (World Scientific, Singapore, 1992); R. Jackiw,Int. J. Mod. Phys. A 3, 285 (1988); A. Shapere and F. Wilczek, eds.,Geometric Phases in Physics (World Scientific, Singapore, 1989).Google Scholar
  11. 11.
    G. Veneziano,Nuovo Cimento A 57, 190 (1968).Google Scholar
  12. 12.
    P. Framton,Dual Resonance Models (Benjamin, New York, 1974).Google Scholar
  13. 13.
    Y. Nambu, inSymmetries and Quark Models, R. Chand, ed. (Gordon & Breach, New York, 1970); H. B. Nielsen and P. Olesen,Phys. Lett. B 32, 203 (1970); L. Susskind,Phys. Rev. D 1, 1182 (1970); O. Hara,Prog. Theor. Phys. 46, 1549 (1971); T. Goto,Prog. Theor. Phys. 46, 1560 (1971).Google Scholar
  14. 14.
    M. Hamermesh,Group Theory (Addison-Wesley, Reading, Massachusetts (1962); V. Bargmann,Ann. Math. 59, 1 (1954); J.-M. Levy-Leblond,J. Math. Phys. 4, 766 (1963).Google Scholar
  15. 15.
    F. Iachello, R. D. Levine, O. S. van Roosmalen,et al., J. Chem. Phys. 77, 3047 (1982);79, 2515 (1983); A. Arima and F. Iachello,Annu. Rev. Nucl. Part Sci. 31, 75 (1981).Google Scholar
  16. 16.
    A. Bohm,Quantum Mechanics: Foundations and Applications, 2nd edn. (Springer, New York, 1979).Google Scholar
  17. 17.
    Appendix V.3 of Ref. 16.Google Scholar
  18. 18.
    P. A. M. Dirac,Can. J. Math. 2, 129 (1950); A. J. Hanson, T. Regge, and C. Teitelboim,Constrained Hamiltonian Systems (Accademia Nazionale dei Lincei, Rome, 1976); Luca Lusanna,Phys. Rep. 185(1), 1 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • A. Bohm
    • 1
  1. 1.Center for Particle Physics, Physics DepartmentThe University of TexasAustin

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