Ivailo M. Mladenov, Vasil V. Tsanov
Reduction in Stages and Complete Quantization of the MIC-Kepler Problem
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

58F06 Geometric quantization (applications of representation theory), See also {22E45, 81S10}

58F07 Completely integrable systems (including systems with an infinite number of degrees of freedom)

81S10 Geometric quantization, symplectic methods, See Also {

Abstract: The one-parameter deformation family of the standard Kepler problem known as the MIC--Kepler problem is completely quantized using the explicit momentum mapping of the torus actions on some toric manifolds and some equivariant cohomology theory. These manifolds appear as symplectic faces of the system. At any level of the reduction process the geometric quantization scheme produces all relevant quantum--mechanical numbers.
Keywords: geometric quantization, equivariant cohomologies