Eine klassische Feldtheorie für die innere Struktur des Elektrons / A Classical Field Theory Describing the Inner Structure of an Electron

Abstract

A theory is given which permits a connection between an inner structure of an electron and the motion of its center of mass obeying Dirac's equation. In order to describe inner properties of the particle a classical nonlinear spinor equation is derived from a Lagrangian. There exist rotational symmetric solutions which are simultaneously finite, stationary, normalizable and strongly localisated, and which yield the mass at rest, the spin and the magnetic moment of the particle in a correct manner. Since these solutions are in contradiction to Heisenberg's uncertainty principle the calculated properties cannot be directly observed in the laboratory system. Therefore an eight-dimensional configuration space is introduced containing the laboratory system and the center-of-masssystem. In this space the wave equation is formulated as a nonlinear differential equation for a spin tensor of second order. If the interaction with an external electromagnetic field is very weak a separation of this tensor equation into the nonlinear spinor equation mentioned above and into Dirac's equation is possible. Observable quantities in the laboratory system can be obtained by integration over the inner coordinates