Semiclassical Quantization of Kowalewski’s Top on 0(4) and 0(3,1) Lie Algebras

  • I. V. Komarov
  • V. B. Kuznetsov
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

We consider a classical dynamical system associated with the Lie algebra g. Its generators J1,x1, ¿=1,2,3 obey the following Poisson brackets (P=constant)
$$\left\{ {{J_1},{J_j}} \right\} = {\varepsilon _{ijk}}{J_{\rm{k}}},\left\{ {{J_{\rm{i}}},{X_j}} \right\} = {\varepsilon _{ijk}}{X_k},\left\{ {{X_i},{X_j}} \right\} = - P{\varepsilon _{ijk}}{J_k}.$$
(1) The Casimir eléments are fixed as follows
$$\ell = \sum\limits_{\rm{i}} {{J_i}{X_i}} ,{a^2} = \sum\limits_{\rm{i}} {({X_{\rm{i}}}{X_{\rm{i}}} - P{J_{\rm{i}}}{J_{\rm{i}}})} .$$
(2)

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References

  1. [1]
    Komarov I. V. 1981 Teor. Mat. Phys. 47 67MathSciNetGoogle Scholar
  2. [2]
    Komarov I. V. and Kuznetsov V. B. 1987 Teor. Mat. Phys. 73 335MathSciNetGoogle Scholar
  3. [3]
    Haine L. and Horozov E. 1987 Physica D 29 173MathSciNetADSMATHCrossRefGoogle Scholar
  4. [4]
    Komarov I. V. and Kuznetsov V. B. 1990 J. Phys. A: Math. Gen. 23 841MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • I. V. Komarov
    • 1
  • V. B. Kuznetsov
    • 1
  1. 1.Department of Computational Physics, Institute of PhysicsLeningrad State UniversityLeningradUSSR

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