Radius of electron as a consequence of Poincaré group

The so-called no-interaction theorem of D.G. Currie, T.F.Jordan, E.C. Sudarshan, H.Leutwyler, G.Marmo and N.Mukunda makes it possible to construct relativistic quasi-classical particle dynamics in the post-Galilean approximation only. We found that in this approximation the Lagrangians are singular on some surfaces of the phase space. The dynamical properties are essentially peculiar on the singular surfaces which we studied. It is shown in this paper that in the case of rectilinear motion of two electrons, the so-called “radius of electron” (the minimal distance between the particles) can be interpreted as the dynamical property of motion on the singular surface generated by the Lagrangian of Darwin.