The center of mass and center of charge of the electron

Abstract

The goal of this contribution is to show that the hypothesis that the center of mass(CM) and the center of charge(CC) of a classical electron are two different points is only compatible with a relativistic description. The existence of two separated points is analyzed by the different dynamical behaviour of the angular momenta with respect to both points. It shows, from the classical point of view, that the angular momentum with respect to the CC of the electron satisfies the same dynamical equation as Dirac spin operator in the quantum case. In the free motion, the CC follows a helix at the speed of light, and the CM the axis of the helix. The particle, if its electromagnetic structure is reduced to a total charge e located at CC, has a magnetic moment and also an electric dipole moment with respect to the CM, like in Dirac's theory. The analysis of Dirac spin operator in the quantum case, shows that the electron is a particle where the CM and CC are necessarily different points.