A Geometric Model in 3+1D Space-Time for Electrodynamic Phenomena
M. Faber
Abstract
With the idea to find geometric formulations of particle physics we investigate the predictions of a three-dimensional generalization of the Sine-Gordon model, very close to the Skyrme model and to the Wu-Yang description of Dirac monopoles. With three rotational degrees of freedom of spatial Dreibeins, we formulate a Lagrangian and confront the predictions to electromagnetic phenomena. Stable solitonic excitations we compare with the lightest fundamental electric charges, electrons, and positrons. Two Goldstone bosons we relate to the properties of photons. These particles are characterized by three topological quantum numbers, which we compare to charge, spin, and photon numbers. Finally, we conjecture some ideas for further comparisons with experiments.