The Creation of Wave Pairs

At the beginning of the paragraph concerning the creation of the plane Involute, we have considered a wave train that is diffracted by the field of an electron in the same way as in Compton effect, and has the wavefront arranged only by one side with respect to the electron's wave field. 
Let us consider indeed a wave train that invests the electron frontally, and that is divided into two parts: one part of the wavefront is diffracted to the right, and the other one to the left. 

The final products are "two" spherical involutes– wave sources, both endowed with opposite Spins, the one that is the mirror image of the other. 

The particle and the antiparticle. 

FIG.19

Is this therefore the phenomenon of the creation of pairs? 

If the wavelength of incident photon is l_i = l_e/2 and the diffracting obstacle is a free electron, we will have the production of an electron and a Dalitz pair formed by a positron and an electron. 

If these two wave structures together with their creative obstacle are subjected to a magnetic field, they will form the three classical traces in a bubble chamber. 

Now, if we subject the propagation of the waves creating the spherical involutes to relativistic conditions, we will have the possibility to justify the Lorentz force from a wave viewpoint, without invoking nor presupposing the existence of the electromagnetic theory at all.