Towards the topological quantization of classical mechanics

TL;DR

This paper adapts topological quantization to classical mechanics, associating systems with fiber bundles and deriving topological spectra that match canonical quantization results.

Contribution

It introduces a novel application of topological quantization to classical systems using Maupertuis' formalism, establishing a new link between topology and classical spectra.

Findings

Topological spectra match canonical spectra for simple systems

Classical systems can be associated with principal fiber bundles

Method extends topological quantization to classical mechanics

Abstract

We consider the method of topological quantization for conservative systems with a finite number of degrees of freedom. Maupertuis' formalism for classical mechanics provides an appropriate scenario which permit us to adapt the method of topological quantization, originally formulated for gravitational field configurations. We show that any conservative system in classical mechanics can be associated with a principal fiber bundle. As an application of topological quantization we derive expressions for the topological spectra of some simple mechanical systems and show that they reproduce the discrete behavior of the corresponding canonical spectra.