Principal Bundles and Topological Quantization of Charges

The space of admissible particle velocities is assumed to be a four-dimensional nonholonomic distribution on a principal or associated bundle. Equations for the horizontal geodesics of this distribution coincide with the equations of motion of charged particles in general relativity theory. It is proved that, if the Lie group of the standard model of elementary particle physics is augmented by the 4-torus, then the wave functions are eigenfunctions of charge operators and the horizontal lift does not depend on the coupling constants. These wave functions satisfy the well-known Dirac equation and its generalizations. For such wave functions, the topological quantization of electric, lepton, and baryon charges takes place.