Quantization of the Linearized Kepler Problem
Guerrero, Julio ; Perez, Jose Miguel
arXiv, 0303037 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-03-14
Classification:  Mathematical Physics,  Mathematics - Symplectic Geometry,  81S10 (Primary) 53D50 (Secondary) 
@article{0303037,
     author = {Guerrero, Julio and Perez, Jose Miguel},
     title = {Quantization of the Linearized Kepler Problem},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0303037}
}

Guerrero, Julio; Perez, Jose Miguel. Quantization of the Linearized Kepler Problem. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0303037/