The second Hopf map and Yang–Coulomb system on a 5D (pseudo)sphere

Stefano Bellucci, Francesco Toppan, Vahagn Yeghikyan
2010 Journal of Physics A: Mathematical and Theoretical  
Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting with a Yang monopole. Then, using a standard trick, we obtain, from the latter system, the pseudospherical and spherical generalizations of the Yang-Coulomb system (the five dimensional analog of MICZ-Kepler system). We present the whole set of its constants of motions, including the hidden symmetry generators given by the analog of Runge-Lenz
more » ... nalog of Runge-Lenz vector. In the same way, starting from the eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the integrable (pseudo)spherical generalization of the Yang-Coulomb system with the Stark term.
doi:10.1088/1751-8113/43/4/045205 fatcat:ef7cw5kkavegtowwd6u3xankha