### Abstract

Using the idea that the symmetry generators commuting with a Landau-like Hamiltonian containing non-Abelian gauge fields will be matrix-valued differential operators, we reconsider the eigenvalue problem of the five-dimensional (5-D) Kepler problem on a SU(2) instanton background. We quickly reproduce the result of Pletyukhov and Tolkachev [J. Math. Phys. 40, 93-100 (1999)], obtained for the energy spectrum. The eigenstates can be expressed in terms of the SU(2) monopole harmonics. The relevance of the theory of induced representations for solving similar problems is emphasized.

Original language | English |
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Pages (from-to) | 7382-7385 |

Number of pages | 4 |

Journal | Journal of Mathematical Physics |

Volume | 41 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2000 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lévay, P. (2000). On the SU(2) Kepler problem.

*Journal of Mathematical Physics*,*41*(11), 7382-7385. https://doi.org/10.1063/1.1285833