The five-dimensional Kepler Problem as an SU(2) Gauge System: Algebraic Constraint Quantization

TL;DR

This paper models the five-dimensional Kepler problem as an SU(2) gauge system and applies an algebraic constraint quantization method based solely on observable quantities.

Contribution

It introduces an SU(2) gauge framework for the 5D Kepler problem and demonstrates a quantization scheme using only observable algebraic constraints.

Findings

Successful gauge description of the 5D Kepler problem

Quantization scheme based on quadratic Casimir observable

Framework applicable to other gauge-analogous systems

Abstract

Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given. This non-abelian gauge system is used as a testing ground for the application of an algebraic constraint quantization scheme which can be formulated entirely in terms of observable quantities. For the quantum mechanical reduction only the quadratic Casimir of the constraint algebra, interpreted as an observable, is needed.