International Journal of Theoretical Physics

, Volume 25, Issue 11, pp 1181–1191 | Cite as

Boson representations of symplectic algebras

  • A. I. Georgieva
  • M. I. Ivanov
  • P. P. Raychev
  • R. P. Roussev
Article
Received:

Abstract

A reduction of the boson representation of the algebra of the noncompact groupSp(4k, R), k>0, to its subgroupSU(k) is realized. The reduction scheme has two main branches: one through the totally symmetric unitary representations of the maximal compact subalgebra u(2k); the other through the ladder representations of the noncompact subalgebrau(k, k). Both reductions are accomplished by means of the same set of Hermitian operators, but taken in different order. The case ofk=3, for the groupSp(12,R), used in the interacting vector boson model, is discussed in more detail.

Keywords

Field Theory Elementary Particle Quantum Field Theory Unitary Representation Reduction Scheme 
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References

  1. Acherova, R. M., Knir, V. A., Smirnov, Yu. F., and Tolstoy, V. N. (1975).Soviet Journal of Nuclear Physics,21, 1126.Google Scholar
  2. Alhassid, Y., Gursey, F., and Iachello, F. (1983).Annals of Physics,148, 346.Google Scholar
  3. Andersen, R. L., Fischer, J., and Raczka, R. (1967).Proceedings of the Royal Society A,302, 491.Google Scholar
  4. Bargmann, V., and Moshinsky, M. (1961).Nuclear Physics,42, 469.Google Scholar
  5. Barut, A. O., and Kleinert, H. (1967).Physical Review,156, 1541.Google Scholar
  6. Barut, A. O., and Raszka, R. (1977).Theory of Group Representations and Applications, PWN, Warsaw.Google Scholar
  7. Dothan, Y., Gell-Mann, M., and Ne'eman, Y. (1965).Physics Letters,17, 148.Google Scholar
  8. Georgieva, A., Raychev, P., and Roussev, R. (1982).Journal of Physics G: Nuclear Physics,8, 1377.Google Scholar
  9. Georgieva, A., Raychev, P., and Roussev, R. (1983).Journal of Physics G: Nuclear Physics,9, 521.Google Scholar
  10. Kibler, M., and Negady, T. (1983a).Nuovo Cimento, Lettere,37, 225.Google Scholar
  11. Kibler, M., and Negadi, T. (1983b).Journal of Physics A: Mathematical and General,16, 4265.Google Scholar
  12. Kibler, M., and Negadi, T. (1984).Physical Review A,29, 2891.Google Scholar
  13. Mack, G., and Todorov, I. (1969).Journal of Mathematical Physics,10, 2078.Google Scholar
  14. Malkin, I. A., and Man'ko, V. I. (1965).JETP Letters,2, 146.Google Scholar
  15. Moshinsky, M. (1962).Review of Modern Physics,34, 813.Google Scholar
  16. Raychev, P. (1972).Soviet Journal of Nuclear Physics,16, 1171.Google Scholar
  17. Rosensteel, G., and Rowe, D. J. (1977a).Physical Review Letters,38, 10.Google Scholar
  18. Rosensteel, G., and Rowe, D. J. (1977b).International Journal of Theoretical Physics,16, 63.Google Scholar
  19. Rosensteel, G., and Rowe, D. J. (1980).Annals of Physics,126, 343.Google Scholar
  20. Todorov, I. T. (1966). ICTP, Trieste, preprint IC/66/71.Google Scholar
  21. Vanagas, V. (1971).Algebraic Methods in Nuclear Theory, Mintis, Vilnius.Google Scholar
  22. Vanagas, V., Nadjakov, E., and Raychev, P. (1975). ICTP, Trieste, preprint IC/75/40.Google Scholar
  23. Varshalovich, D. A., Moskalev, A. N., and Hersonsky, V. K. (1975).Quantum Theory of Angular Momentum, Nauka, Leningrad.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • A. I. Georgieva
    • 1
  • M. I. Ivanov
    • 1
  • P. P. Raychev
    • 1
  • R. P. Roussev
    • 1
  1. 1.Institute of Nuclear Research and Nuclear EnergyBulgarian Academy of SciencesSofiaBulgaria

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