On the manifestation of the cosmological curvature of space in a model of a neutral fermion with three mass parameters

In this work a generalized fermion model with spin $1/2$, which is characterized by three physical mass parameters $M_i$ are studied. The additional interaction is determined by the tensor of the external electromagnetic field and the scalar space-time curvature. It joints three bispinors into one physical system. The model also remains valid for neutral Majorana fermions. The coupling of three bispinors into a single system is ensured by the nonzero scalar curvature of the space-time. We study a model situation where it can be assumed that locally the use of Cartesian coordinates is permissible, and the external geometric background can be effectively taken into account by a constant Ricci curvature $R$. For simplicity, we restrict ourselves to the one-dimensional case $(t, x)$. Using the diagonalization of the mixing matrix in a complex system of equations, we reduce the problem to three separate Dirac-type equations with new effective masses $\overline{M}_i$, the values of which are determined numerically depending on the internal parameter of the model and the space-time curvature. A numerical analysis of the necessary diagonalizing transformations $S$ and $S^{-1}$ is given. The solutions of three separate equations of the Majorana type are constructed in the momentum-helicity basis. Using the expression for the transformation matrices $S$ and $S^{-1}$, these solutions are decomposed into linear combinations by solutions with physical masses and vice versa.