General classical theory of spinning particles in a Maxwell field

Abstract

The purpose of this paper is to give the complete classical theory of a spinning particle moving in a Maxwell field. The particle is assumed to be a point, and its interaction with the field is described by a point charge g 1 and a point dipole g 2 . The Maxwell equations are assumed to hold right up to the point representing the particle. Exact equations are then derived for the motion of the particle in a given external field which are strictly consistent with the conservation of energy, momentum and angular momentum, and hence contain the effects of radiation reaction on the motion of the particle. It is shown that in the presence of a point dipole the energy tensor of the field can and must be redefined so as to make the total energy finite. The mass, the angular momentum of the spin, and the moment of inertia perpendicular to the spin axis appear in the equations as arbitrary mechanical constants. Reasons are given for believing that for an elementary particle the last constant is zero, in agreement with relativistic quantum theory. In the general theory there is no relation between the electric and magnetic dipole moments of the particle and the state of its translational motion. A procedure is given for deriving from the general equations specialized equations consistent with the condition that the dipole is always a purely magnetic or electric one in the system in which the particle is instantaneously at rest. The radiation reaction terms are very much simpler in the former of these specialized cases than in the general case. The effect of radiation reaction is to make the scattering of light by a rotating dipole decrease inversely as the square of the frequency for high frequencies, just as for scattering by a point charge.