Spin Effects on the Cyclotron Frequency for a Dirac Electron

The Barut–Zanghi (BZ) theory can be regarded as the most satisfactory picture of a classical spinning electron and constitutes a natural “classical limit” of the Dirac equation. The BZ model has been analytically studied in some previous papers of ours in the case of free particles. By contrast, in this letter we consider the case of external fields, and a previously found equation of the motion is generalized for a non-free spin2 particle. In the important case of a spinning charge in a uniform magnetic field, we find that its angular velocity (along its circular orbit around the magnetic field direction) is slightly different from the classical “cyclotron frequency” ωclass ≡ eH/m which is expected to hold for spinless charges. As a matter of fact, the angular velocity does depend on the spin orientation. As a consequence, the electrons with magnetic moment μ parallel to the magnetic field do rotate with a frequency greater with respect to electrons endowed with a μ antiparallel to H . PACS numbers: 03.65.-w; 03.65.Sq; 14.60.Cd (†) Work supported by INFN and by CNPq.