XXVI Workshop on Geometric Methods in Physics 1-7.07.2007

Francisco Nettel-Rueda

Topological quantization of classical mechanics (Francisco Nettel and Hernando Quevedo)

We extend the method of topological quantization to classical conservative systems with a finite number of degrees of freedom described within the Maupertuis formalism. We show that a principal fiber bundle can be constructed for these systems with the reduced Galilean group as the fiber (as the structure group). Finally we analyze the harmonic oscillator and derive an expression for what we call the topological spectrum.