A Generalization of the Kepler Problem

TL;DR

This paper introduces a broad class of generalized Kepler problems parameterized by dimension, curvature, and magnetic charge, extending classical Kepler dynamics through spinor and monopole analogues.

Contribution

It constructs a new family of Kepler problems using Young powers of fundamental spinors, generalizing classical models with novel geometric and algebraic structures.

Findings

New generalized Kepler problems parameterized by (D, κ, μ)

Identification of spinor Young powers as analogues of Dirac monopoles

Framework unifies classical and magnetic monopole Kepler problems

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.