Communications in Mathematical Physics

, Volume 26, Issue 3, pp 222–236 | Cite as

Coherent states for arbitrary Lie group

  • A. M. Perelomov


The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Coherent State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Glauber, R. J.: Phys. Rev.130, 2529 (1963);131, 2766 (1963).Google Scholar
  2. 2.
    Klauder, J. R., Sudarshan, E. C. G.: Fundamentals of quantum optics. New York: Benjamin 1968.Google Scholar
  3. 3.
    Zeldovich, B. Ya., Perelomov, A. M., Popov, V. S.: JETP55, 589 (1968);57, 196 (1969); Preprints ITEP No.612, 618 (1968).Google Scholar
  4. 4.
    Weyl, H.: Gruppentheorie und Quantenmechanik. Leipzig: S. Hirzel 1928.Google Scholar
  5. 5.
    Barut, A. O., Girardello, L.: Commun. math. Phys.21, 41 (1971).Google Scholar
  6. 6.
    Mackey, G. W.: Bull. Am. Math. Soc.69, 628 (1963).Google Scholar
  7. 7.
    Perelomov, A. M.: Theoret. Math. Phys.6, 213 (1971).Google Scholar
  8. 8.
    Cartier, P.: Symp. Pure Math., v. 9, Algebraic groups and discontinuous subgroups, p. 361. Providence, R.I.: Amer. Math. Soc. 1966.Google Scholar
  9. 9.
    Gelfand, I. M., Minlos, R. A., Shapiro, Z. Ya.: Representations of the rotation group and the Lorentz group. Oxford: Pergamon Press 1963.Google Scholar
  10. 10.
    Vilenkin, N. Ya.: Special functions and the theory of group representations. Providence, R.I.: Amer. Math. Soc. 1968.Google Scholar
  11. 11.
    Bargmann, V.: Ann. Math.48, 568 (1947).Google Scholar
  12. 12.
    —— Comm. Pure Appl. Math.14, 187 (1961).Google Scholar
  13. 13.
    Perelomov, A. M.: Theoret. Math. Phys.6, 368 (1971).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • A. M. Perelomov
    • 1
  1. 1.Institute for Theoretical and Experimental PhysicsMoscowUSSR

Personalised recommendations