Geometric quantization of the MIC-Kepler problem via extension of the phase space
Mladenov, Ivailo M.
Annales de l'I.H.P. Physique théorique, Tome 51 (1989), p. 219-227 / Harvested from Numdam
Publié le : 1989-01-01
@article{AIHPA_1989__50_2_219_0,
     author = {Mladenov, Ivailo M.},
     title = {Geometric quantization of the MIC-Kepler problem via extension of the phase space},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {51},
     year = {1989},
     pages = {219-227},
     mrnumber = {1002821},
     zbl = {0695.70006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1989__50_2_219_0}
}
Mladenov, Ivailo M. Geometric quantization of the MIC-Kepler problem via extension of the phase space. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) pp. 219-227. http://gdmltest.u-ga.fr/item/AIHPA_1989__50_2_219_0/

[1] J. Marsden, A. Weinstein, Reduction of Symplectic Manifolds with Symmetry. Rep. Math. Phys., vol. 5, 1974, p. 121-130. | MR 402819 | Zbl 0327.58005

[2] B. Kostant, Quantization and Unitary Representations, Lecture Notes in Mathematics, vol. 170, 1970, p. 87-208. | MR 294568 | Zbl 0223.53028

[3] J.M. Souriau, Structure des Systèmes Dynamiques, Dunod, Paris, 1970. | MR 260238 | Zbl 0186.58001

[4] M. Puta, On the Reduced Phase Space of a Cotangent Bundle. Lett. Math. Phys., t. 8, 1984, p. 189-194. | MR 750032 | Zbl 0557.58012

[5] V. Guillemin, S. Sternberg, Geometric Quantization and Multiplicities of Group Representations. Invent. Math., t. 67, 1982, p. 515-538. | MR 664118 | Zbl 0503.58018

[6] M. Gotay, Constraints, Reduction and Quantization. J. Math. Phys., t. 27, 1986, p. 2051-2066. | MR 850590 | Zbl 0632.58020

[7] M. Kummer, On the Construction of the Reduced Phase Space of a Hamiltonian System with Symmetry. Indiana Univ. Math. J., t. 30, 1981, p. 281-291. | MR 604285 | Zbl 0425.70019

[8] R. Abraham, J. Marsden, Foundation of Mechanics. Benjamin, Mass. 1978.

[9] G. Marmo, E. Saletan, A. Simoni, B. Vitale, Dynamical Systems. A Différential Geometric Approach to Symmetry and Reduction, Wiley, Chichester, 1985. | MR 818988 | Zbl 0592.58031

[10] P. Libermann, C.-M. Marle, Symplectic Geometry and Analytical Mechanics, Reidel, Dordrecht, 1987. | MR 882548 | Zbl 0643.53002

[11] T. Iwai, Y. Uwano, The Four-Dimensional Conformal Kepler Problem Reduces to the Three-Dimensional Kepler Problem with a Centrifugal Potential and Dirac's Monopole Field. Classical Theory. J. Math. Phys., t. 27, 1986, p. 1523-1529. | MR 843720 | Zbl 0599.70015

[12] I. Mladenov, V. Tsanov, Geometric Quantisation of the MIC-Kepler Problem. J. Phys. A. Math. Gen., t. 20, 1987, p. 5865-5871. | MR 939893 | Zbl 0658.58051

[13] M. Kibler, T. Negadi, The Use of Nonbijective Canonical Transformations in Chemical Physics. Croatica Chem. Acta, t. 57, 1984, p. 1509-1523.

[14] L. Davtyan, L. Mardoyan, G. Pogosyan, A. Sissakian, V. Ter-Antonyan, Generalized KS Transformation: From Five-Dimensional Hydrogen Atom to EightDimensional Isotrope Oscillator. J. Phys. A. Math. Gen., t. 20, 1987, p. 6121-6125. | MR 939909

[15] L. Bates, Ph.D. Thesis, University of Calgary, 1988.

[16] B. Cordani, L. Feher, P. Horvathy, Monopole Scattering Spectrum from Geometric Quantisation. J. Phys. A. Math. Gen., t. 21, 1988, p. 2835-2837. | MR 953452 | Zbl 0672.58054