A spin 1/2 particle with anomalous magnetic and electric dipole moments

Abstract

It is Petras who first developed the P-symmetric theory for a spin 1/2 particle with an anomalous magnetic moment within the general Gel’fand – Yaglom approach. Recently, similarly it was introduced a P-asymmetric wave equation for a spin 1/2 particle which describes a particle with an electric dipole moment. In this paper, we study solutions of the equation for the P-asymmetric particle in presence of external magnetic fields. It turns out that the energy spectra are the same for P-asymmetric and P-symmetric particles. To clarify this coincidence, we demonstrate that there exists a simple transformation relating these two models, by which one wave equation can be reduced to the form of the other. Meanwhile, expressions for wave functions and P-reflection operators are different in these two theories. We extend this approach to the model in which both P-symmetric and P-asymmetric sectors are presented. The main result is the same, namely, there exists a simple, more general as compared with the mentioned above transformation relating the P-symmetric model and the model with two sectors, and expressions for wave functions and P-reflection operators are different in these two bases. We demonstrate that in the presence of an external uniform magnetic field, the energy spectra in the model with two sectors coincide with those in the P-symmetric theory. Thus, we develop a general theory for the P-asymmetric model and the model with two sectors within the Petras approach.