(3+0)D electromagnetic solitons and de Broglie's ''double solution''

Abstract

The well known light filaments are obtained in various media whose index of refraction increases before a saturation with the electric field; adding a small perturbation which increases the index with the magnetic field, and neglecting the absorption, a filament curves and closes into a torus. This transformation of a (2+1)D soliton into a (3+0)D soliton shows the existence of those solitons, while a complete study, with a larger magnetic effect, would require numerical computations, the starting point being, possibly, the perturbed, curved filament. The flux of energy in the regular filaments is nearly a ''critical flux'', depending slightly on the external fields, so that the energy of the (3+0)D soliton is quantified, but may be slightly changed by external interactions. The nearly linear part of the soliton, an evanescent wave, is partly transmitted by Young holes, making transmitted and reflected interference patterns, thus index variations which guide the remainder of the soliton, just as de Broglie's pilot waves. The creation of electron positron pairs in the vacuum by purely electromagnetic fields shows a nonlinearity of vacuum at high energies; supposing this nonlinearity convenient, elementary particles may be (3+0)D solitons or light bullets, so that it may be a connection with the superstrings theory.