On the equations of motion of point particles

Abstract

The equations of motion of a point particle, possessing a charge, dipole or higher multipole moments and having an interaction with a generalized wave field of an arbitrary integral spin, are obtained explicitly. These equations are independent of the particular choice of the energy-momentum tensor of the field from among the many alternatives given by Fierz. A convenient method for the calculation of the radiation field is given. The definition of the spin of the particle is given, and it is postulated that the magnitude of this spin is constant. It is shown that this assumption effects a great simplification in the equations of a charged dipole in a vector-meson field. The equations are determined completely in terms of two arbitrary constants which are to be interpreted as the mass and the spin. Further, it is shown that only those dipoles for which the ‘electric’ and the ‘magnetic’ moments are parallel in the rest system are consistent with this assumption. The equations of motion of a charged dipole in a scalar-meson field are derived. These equations also contain only two arbitrary constants which again are to be interpreted as the mass and the spin.