Within the general method by Gel’fand-Yaglom, starting with the extended 28-component representation of the Lorentz group (it includes four bispiniors and one spinor of the 3rd rank), for a spin 1/2 particle, we construct a relativistic P-invariant generalized system of the first order equations for a spin 1/2 particle with three additional to electric charge characteristics. First, the model is developed for a free particle, and the system of spinor equations is derived; then it is transformed to spin-tensor form. In this spin-tensor form, we take into account the presence of external electromagnetic fields. After eliminating the accessory variables of the complete wave function, we derive the minimal 4-component Dirac-like equation, the last includes several new interaction terms which are interpreted as related to some additional electromagnetic characteristics of a spin 1/2 particle.
Kisel et al. (Wed,) studied this question.