A generalization of the Kepler problem

A generalization of the Kepler problem is constructed and analyzed. These generalized Kepler problems are parametrized by a triple (D, κ, μ), where the dimension D is an integer ≥3, the curvature κ is a real number, and the magnetic charge μ is a half-integer if D is odd and zero or half if D is even. The key to constructing 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 analogs of the Dirac monopoles. The text was submitted by the authors in English.