The Kepler problem spinor regularization and pre-quantization of the negative-energy manifold

Mathematics

Scientific paper

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Kepler Laws, Manifolds, Orbital Mechanics, Perturbation Theory, Quantum Mechanics, Spinor Groups, Angular Momentum, Hamiltonian Functions, Singularity (Mathematics)

Scientific paper

The spinor-matrix form derived by Vivarelli (1981 and 1984) for the KS map (Kustaanheimo and Steifel, 1965) of the three-dimensional Kepler problem is extended and refined. A natural spinor extension of the KS regularization to the entire phase space of the problem is developed and applied to the prequantization of the manifold of negative-isoenergetic Kepler orbits. The quantized manifold is shown to be diffeomorphic to the symplectic product of two three-spheres of the spinor phase space when the appropriate equivalence relation is employed. The value of the present analysis in simplifying numerical computations of Kepler orbits in perturbation theory, while avoiding the use of hard-to-understand ad hoc mathematical devices, is indicated.

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