Topological spectrum of classical configurations

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.