Abstract
The manifoldM of null rays through the origin of ℙ2,n+1 is diffeomorphic toS 1×S n, and it is a homogeneous space of SO(2,n+1). This group therefore acts onT*M, which we show to be the “generating manifold” of the extended phase space of the regularized Kepler Problem. A local canonical chart inT*M is found such that the restriction to the subbundle of the null nonvanishing covectors is given byp 0+H(q,p)=0, whereH(q,p) is the Hamiltonian of the Kepler Problem. By means of this construction, we get some results that clarify and complete the previous approaches to the problem.
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Communicated by S.-T. Yau
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Cordani, B. Conformal regularization of the Kepler Problem. Commun.Math. Phys. 103, 403–413 (1986). https://doi.org/10.1007/BF01211755
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DOI: https://doi.org/10.1007/BF01211755