Dirac particle in the presence of wave fields against gravitational background

In the present work the problem of exact description of the Dirac particle interacting with external wave fields on the gravitational background has been studied. Some new exact solutions are presented. Different geometrical realizations of the tensor connection inclusion coupled with scalar or pseudoscalar wave are considered. The separation of variables providing possibilities for exact solution in the corresponding field situations is carried out in the frame work of the algebraic method. Simultaneously the most general metrics allowing exact solutions of the Dirac equation have been found. Both cases of the non-zero rest mass of particle are considered