Skip to main content
Log in

Finite transformations of SU(4)

  • Published:
Czechoslovak Journal of Physics B Aims and scope

Abstract

The problem of determining the representation matrices of SU(4) is investigated. A convenient set of parameters is first introduced by writing the general element of the group as a product of exponential functions of the generators, and the generators are expressed as differential operators involving these parameters. Special matrix elements of finite transformations with a SU(3) singlet as the initial state are then obtained by solving the eigenvalue equation of the quadratic Casimir operator of SU(4). The solution has the form of a product of elementary functions and threed jm′m functions of SU(2) and is free from summation over intermediate states. By expanding one of thed jm′m functions in an appropriate series a sum rule for the special matrix elements of the permutation operator 1234→3412 is obtained. The discussions are strictly confined to SU(4), but, some of the results given here can be extended to unitary groups of higher dimensions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Wigner E. P., Phys. Rev.51 (1937), 106.

    Google Scholar 

  2. Burdet G., Maguin C., Partensky A., Nuovo CimentoB 54 (1968), 1;B 64 (1969), 263.

    Google Scholar 

  3. Louck J. D., Galbraith H. W., Rev. Mod. Phys.44 (1972), 540.

    Google Scholar 

  4. Antoine J. P., Speiser D., Oakes R. J., Phys. Rev.141 (1966), 1542.

    Google Scholar 

  5. Kobayashi M., Nakagawa M., Nitto H., Progr. Theor. Phys.47 (1972), 982.

    Google Scholar 

  6. Nelson T. J., J. Math. Phys.8 (1967), 857.

    Google Scholar 

  7. Majumdar S. D., Progr. Theor. Phys.42 (1969), 1475.

    Google Scholar 

  8. Majumdar S. D.,Basu B. K., J. Math. Phys. (to be published).

  9. Majumdar S. D., Basu B. K., Ann. of Phys.56 (1970), 464.

    Google Scholar 

  10. Flores J., Niederle J., Czech. J. Phys.B 20 (1970), 1241.

    Google Scholar 

  11. Ciftan M., Biedenharn L. C., J. Math. Phys.10 (1969), 221.

    Google Scholar 

  12. Ciftan M., Math. Phys.10 (1969), 1635.

    Google Scholar 

  13. Jakimow G., Sharp R. T., Canad. J. Phys.47 (1969), 2137.

    Google Scholar 

  14. Sen R. N., J. Math. Phys.8 (1967), 896.

    Google Scholar 

  15. Wu A. C. T., J. Math. Phys.12 (1971), 437.

    Google Scholar 

  16. Yutsis A. P., Levinson I. B., Vanagas V. V., Mathematical Apparatus of the Theory of Angular Momentum. Israel Program for Scientific Translations, Jerusalem, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Basu, B.K., Majumdar, S.D. Finite transformations of SU(4). Czech J Phys 23, 1149–1158 (1973). https://doi.org/10.1007/BF01591196

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01591196

Keywords

Navigation