Galactic Dynamics in the Siegel Half-Plane

  • G. Rosensteel

Abstract

The dynamics of rotating galaxies is modeled by a Hamiltonian Lax system for which the phase space is a homogeneous G-manifold with the Lie group G equal to either the noncompact real symplectic group Sp(n, R) or a maximal parabolic subgroup GCM(n). The dimensions n = 1, 2, 3 correspond respectively to breathing mode oscillations, planar rotations, and three-dimensional collective motion. The homogeneous GCM(3)-manifolds correspond to the Riemann ellipsoids. The homogeneous G-manifold Sp(n, R)/U(n), where U(n) is the maximal compact subgroup, is a classical complex domain diffeomorphic to the Siegel upper half-plane S n . Equilibrium galactic radii are determined for S 1 systems.

Keywords

Manifold 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Chandrasekhar, “Ellipsoidal Figures of Equilibrium, Yale University Press, New Haven (1969)MATHGoogle Scholar
  2. 2.
    P. Lax, Commun. Pure Appl. Math. 21: 467 (1968)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Ju. Moser, Adv. Math. 16: 197 (1975)ADSMATHCrossRefGoogle Scholar
  4. 4.
    James Binney and Scott Tremaine, “Galactic Dynamics”, Princeton University Press, Princeton (1987)MATHGoogle Scholar
  5. 5.
    G. Rosensteel, Lax representation of Riemann ellipsoids, Appl. Math. Lett. 6: 55 (1993)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    G. Rosensteel, Rapidly rotating nuclei as Riemann ellipsoids, Ann. Phys. (N.Y.) 186: 230 (1988)MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    G. Rosensteel and E. Ihrig, Geometric quantization of the CM(3) Model, Ann. Phys. (N.Y.) 121: 113 (1979)MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    G. Rosensteel and E. Ihrig, Geometric quantization of Riemann rotors, in: “Geometric Quantization and Coherent States Methods”, S. Twareque Ali, I.M. Mladenov, and A. Odzijewicz (eds.), World Scientific, Singapore (1993)Google Scholar
  9. 9.
    G. Rosensteel, Self-gravitating symplectic systems, Astrophys. J. 416: 291 (1993).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • G. Rosensteel
    • 1
  1. 1.Physics DepartmentTulane UniversityNew OrleansUSA

Personalised recommendations