Armen Nersessian and Armen Yeranyan 2004 J. Phys. A: Math. Gen. 37 2791 doi:10.1088/0305-4470/37/7/020
Armen Nersessian1,2 and Armen Yeranyan2
Show affiliationsWe define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kähler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kähler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid originate. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to a monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is a non-Kähler one. Finally, we extend these results to the family of Kähler spaces with conic singularities.
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
Issue 7 (20 February 2004)
Received 23 October 2003
Published 4 February 2004
Armen Nersessian and Armen Yeranyan 2004 J. Phys. A: Math. Gen. 37 2791
J Jansen and H B Zeedijk 1972 J. Phys. E: Sci. Instrum. 5 973
G Varoquaux et al 2009 New J. Phys. 11 113010
S Ozer and C Besikci 2003 J. Phys. D: Appl. Phys. 36 559
Michael Pycraft Hughes 2000 Nanotechnology 11 124
A Parker 2006 Inverse Problems 22 599
Firmi P Banzi et al 2000 J. Radiol. Prot. 20 41
S Anantha Ramakrishna 2005 Rep. Prog. Phys. 68 449
Tomasz Pawlowski et al 2004 Class. Quantum Grav. 21 1237
F Hayot and C Jayaprakash 2004 Phys. Biol. 1 205