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.
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References
Acherova, R. M., Knir, V. A., Smirnov, Yu. F., and Tolstoy, V. N. (1975).Soviet Journal of Nuclear Physics,21, 1126.
Alhassid, Y., Gursey, F., and Iachello, F. (1983).Annals of Physics,148, 346.
Andersen, R. L., Fischer, J., and Raczka, R. (1967).Proceedings of the Royal Society A,302, 491.
Bargmann, V., and Moshinsky, M. (1961).Nuclear Physics,42, 469.
Barut, A. O., and Kleinert, H. (1967).Physical Review,156, 1541.
Barut, A. O., and Raszka, R. (1977).Theory of Group Representations and Applications, PWN, Warsaw.
Dothan, Y., Gell-Mann, M., and Ne'eman, Y. (1965).Physics Letters,17, 148.
Georgieva, A., Raychev, P., and Roussev, R. (1982).Journal of Physics G: Nuclear Physics,8, 1377.
Georgieva, A., Raychev, P., and Roussev, R. (1983).Journal of Physics G: Nuclear Physics,9, 521.
Kibler, M., and Negady, T. (1983a).Nuovo Cimento, Lettere,37, 225.
Kibler, M., and Negadi, T. (1983b).Journal of Physics A: Mathematical and General,16, 4265.
Kibler, M., and Negadi, T. (1984).Physical Review A,29, 2891.
Mack, G., and Todorov, I. (1969).Journal of Mathematical Physics,10, 2078.
Malkin, I. A., and Man'ko, V. I. (1965).JETP Letters,2, 146.
Moshinsky, M. (1962).Review of Modern Physics,34, 813.
Raychev, P. (1972).Soviet Journal of Nuclear Physics,16, 1171.
Rosensteel, G., and Rowe, D. J. (1977a).Physical Review Letters,38, 10.
Rosensteel, G., and Rowe, D. J. (1977b).International Journal of Theoretical Physics,16, 63.
Rosensteel, G., and Rowe, D. J. (1980).Annals of Physics,126, 343.
Todorov, I. T. (1966). ICTP, Trieste, preprint IC/66/71.
Vanagas, V. (1971).Algebraic Methods in Nuclear Theory, Mintis, Vilnius.
Vanagas, V., Nadjakov, E., and Raychev, P. (1975). ICTP, Trieste, preprint IC/75/40.
Varshalovich, D. A., Moskalev, A. N., and Hersonsky, V. K. (1975).Quantum Theory of Angular Momentum, Nauka, Leningrad.
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Georgieva, A.I., Ivanov, M.I., Raychev, P.P. et al. Boson representations of symplectic algebras. Int J Theor Phys 25, 1181–1191 (1986). https://doi.org/10.1007/BF00668689
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DOI: https://doi.org/10.1007/BF00668689