  The linearized Kepler problem is considered, as obtained from the
Kustaanheimo-Stiefel (K-S)transformation, both for negative and positive
energies. The symmetry group for the Kepler problem turns out to be SU(2,2).
For negative energies, the Hamiltonian of Kepler problem can be realized as the
sum of the energies of four harmonic oscillator with the same frequency, with a
certain constrain. For positive energies, it can be realized as the sum of the
energies of four repulsive oscillator with the same (imaginary) frequency, with
the same constrain. The quantization for the two cases, negative and positive
energies is considered, using group theoretical techniques and constrains. The
case of zero energy is also discussed.
