Conformal regularization of the Kepler Problem

The manifoldM of null rays through the origin of ^2,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.