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Galactic Dynamics in the Siegel Half-Plane

In: Quantization, Coherent States, and Complex Structures

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  • G. Rosensteel

    (Tulane University, Physics Department)

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.

Suggested Citation

  • G. Rosensteel, 1995. "Galactic Dynamics in the Siegel Half-Plane," Springer Books, in: J.-P. Antoine & S. Twareque Ali & W. Lisiecki & I. M. Mladenov & A. Odzijewicz (ed.), Quantization, Coherent States, and Complex Structures, pages 271-279, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1060-8_31
    DOI: 10.1007/978-1-4899-1060-8_31
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