On the Possible Trajectories of Spinning Particles in an External Electromagnetic Fields

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 depend- ing from both position and the state of movement, as well as by two pseudo-vectors one of which is easily associated with external magnetic field, and another still remains undetermined. It is shown that description of the motion of both massive and massless particles with spin is possible. All solu- tions of the equations of motion of spinning particle 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 ellipses around fixed centers of balance, with the spin of particles can have any direction. The behavior of spin particles in a constant homogeneous magnetic field is also considered and all types of trajectories are found.