New equation for a spin 1/2 particle with three additional characteristics in presence of electromagnetic and gravitational fields

Abstract

Within the general Gel’fand–Yaglom method, starting from the extended 28-component representation of the Lorentz group, we construct a new relativistic P-invariant generalized equation for a spin-1/2 particle possessing three characteristics in addition to the electric charge. The model is first developed for a free particle, where the corresponding system of spinor equations is derived and then transformed into spin-tensor form. In this form, we incorporate the interaction with external electromagnetic fields. By eliminating the accessory variables of the complete wave function, we obtain a minimal four-component Dirac-like equation that contains three new interaction terms, interpreted as arising from the additional electromagnetic characteristics of the particle. This approach is further extended to a Riemann space–time background within the conventional tetrad formalism, leading to additional geometrical interaction terms involving the Ricci scalar R(x), the Ricci tensor Rαβ, and the Riemann curvature tensor Rαβρσ(x).