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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics