How to Describe Photons as (3+1)-Solitons?

Abstract

This paper aims to present the pure field part of the newly developed nonlinear {\it Extended Electrodynamics} [1]-[3] in non-relativistic terms, i.e. in terms of the electric and magnetic vector fields (${\mathbf E},{\mathbf B}$), and to give explicitly those (3+1)-soliton solutions of the new equations which have the integral properties of photons. The set of solutions to the new equations contains all solutions to Maxwell's equations as a subclass, as well as, new solutions, called nonlinear. The important characteristics {\it scale factor}, {\it amplitude function}, and {\it phase function} of a nonlinear solution are defined in a coordinate free way and effectively used. The nonlinear solutions are identified through the non-zero values of two appropriately defined vector fields $\vec{\cal F}$ and $\vec{\cal M}$, as well as, through the finite values of the corresponding scale factors. The intrinsic angular momentum (spin) is also defined. A limited superposition principle (interference of nonlinear solutions), yielding the well known classical {\it coherence} conditions, is found to exist.