It is shown that the 5D Ricci identities give us a way to create a new viewpoint on the origin of the Maxwell equations, magnetic monopole problem, and also on some problems of the Astrophysics and Cosmology. Specifically, the application of the identities together with the monad and dyad methods makes it possible to introduce the new concept of the rest mass of the elementary particles. The latter leads to the new connections between the General Relativity and quantum field theories, as well as to a better understanding of the magnetic monopole problem and the origins of the Maxwell equations. The obtained results also provide a new insight into the mechanism of the accelerated expansion of the 4D Universe.
ON POSSIBLE GEOMETRIC AND ASTROPHYSICAL EFFECTS OF NONLINEAR SPINOR FIELDS IN THE MEGAMIR, MACROWORLD AND MICROWORLD