A Generalization of the Kepler Problem

We construct and analyze a generalization of the Kepler problem. These generalized Kepler problems are parameterized by a triple $(D, κ, μ)$ where the dimension $D\ge 3$ is an integer, the curvature $κ$ is a real number, the magnetic charge $μ$ is a half integer if $D$ is odd and is 0 or 1/2 if $D$ is even. The key to construct these generalized Kepler problems is the observation that the Young powers of the fundamental spinors on a punctured space with cylindrical metric are the right analogues of the Dirac monopoles.

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