On the Possible Trajectories of Spinning Particles. I. Free Particles

Abstract

By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as well as by two pseu- do-vectors one of which is easily associated with external magnetic field, and another still remains undetermined. The equations give a possibility to describe the motion of both mas- sive and massless particles with spin. All solutions of the equations of motion in the absence of external fields were found, and besides, we give more precise definition of a free object. It turns out that the massive particles always possess a longitudinal polarization. There are possible transversal motions of the following types: 1) oscillatory motion with proper frequency, 2) circular motion, and 3) complicated motion along rosette trajectories round the center of inertia with the velocity, varying in the limits vmin v vmax . Free massless particles can either fluctuate or move along complicated paths around fixed centers of balance, when the spin of the particles can have any direction.