Fermion with three mass parameters: interaction with external fields
In the article, using the Gelfand-Yaglom general approach, a new 20-component wave equation for spin 1/2 fermion that is characterized by three mass parameters is derived. Based on the 20-component wave function three auxiliary bispinors are determined, in the absence of an external field, these bispinors obey three separate Dirac-like equations with different masses M1, M2, M3. In the presence of external electromagnetic fields, the main equation is not split into the separated equations; instead quite definite mixing of three Dirac-like equations arises. The model is extended to the curved space-time background. If the scalar space curvature differs from zero, then additional terms of geometrical interaction occur between three bispinor components. The model for fermion with three mass parameters allows for the restriction to the case of the neutral Majorana particle.