Classical Theory of Charged Point-Particles with Dipole Moments

The theory of the point electron given by one of the authors (Schönberg) is extended to the case of point particles with dipole moments. The stress tensor of the field contains new terms which do not exist in the case of particles without dipole moments. These terms make the stress tensor asymetrical and give raise to torques acting on the spins of the particles. The equations of motion are derived by using a generalized form of a method given by Frenkel, which takes into account the coupling between spin rotation and translational motion due to the special character of the spin tensor. The variational principle of Tetrode and Fokker is extended to the motion of point particles with magnetic moment, in a form which takes into account the reaction of radiation and the coupling between spin rotation and translational motion. It is shown that the hamiltonian formalism can be extended to the particles in consideration. The Poisson Brackts for the spin components are computed and correspond to those given by Dirac’s quantum theory of the electron, though differing from those given by Kramers, which are shown to be insatisfactory.