Conformal regularization of the Kepler Problem

Details Conformal regularization of the Kepler Problem Conformal regularization of the Kepler Problem

Sep 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cmaph.103..403c&link_type=abstract

Communications in Mathematical Physics, Volume 103, Issue 3, pp.403-413

Mathematics

Mathematical Physics

17

Scientific paper

The manifold M of null rays through the origin of ℙ2, n+1 is diffeomorphic to S 1× S n , and it is a homogeneous space of SO(2, n+1). This group therefore acts on T*M, which we show to be the “generating manifold” of the extended phase space of the regularized Kepler Problem. A local canonical chart in T*M is found such that the restriction to the subbundle of the null nonvanishing covectors is given by p 0+ H(q,p)=0, where H(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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