A Generalization of the Kepler Problem

Abstract

We construct and analyze a generalization of the Kepler problem. These generalized Kepler problems are parameterized by a triple $(D,\kappa ,\mu )$ where the dimension $D\ge 3$ is an integer, the curvature $\kappa$ is a real number, the magnetic charge $\mu$ 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.

The final version. To appear in J. Yadernaya fizika

References in corpus (1)

• Essential self-adjointness of Schroedinger type operators on manifolds

Cited by in corpus (1)

• Algebraic structure underlying spherical, parabolic and prolate spheroidal bases of the nine-dimensional MICZ-Kepler problem