Effects of spin on the cyclotron frequency for a Dirac electron

The Barut–Zanghi (BZ) theory – that constitutes a natural `classical limit' of the Dirac theory and can be regarded to be a satisfactory picture of a classical spinning electron – 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 motion is generalized for a non-free spin-12 particle. In the important case of a spinning charge in a uniform magnetic field, we find that its angular frequency (around the magnetic field direction) is slightly different from the classical `cyclotron frequency' ω≡eH/m expected for spinless charges. As a matter of fact, the angular frequency 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 than that of electrons endowed with a μ antiparallel to H.