Topological spectrum of classical configurations

TL;DR

This paper introduces the topological spectrum as a new way to analyze classical configurations using topological invariants derived from fiber bundles, providing a discretization of parameters.

Contribution

It proposes a novel concept linking classical configurations to fiber bundle topology, offering a new perspective on their parameter discretization.

Findings

Topological spectrum relates parameters of classical configurations via topological invariants.

Examples demonstrate the procedure and significance of the topological spectrum.

The approach provides a geometric and topological framework for classical systems.

Abstract

For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a principle fiber bundle that contains all the physical and geometric information of the configuration. The topological spectrum follows from the investigation of the corresponding topological invariants. Examples are given which illustrate the procedure and the significance of the topological spectrum as a discretization relationship among the parameters that determine the physical meaning of classical configurations.