Fermion fields in theories of gravitation

After an introduction to the formalism used throughout the paper there follows a concise presentation of the theory of fermion fields in one-tetrad gravitational theories. That presentation gives a hint to the construction of a bi-tetrad theory, the two tetrad fields being denoted by hsup(A) sub(k) and anti hsup(A) sub(k). The tetrad field hsup(A) sub(k) gives the Riemannian metric gsub(kl) while the tetrad field anti hsup(A) sub(k) is orthonormalized with respect to the flat metric asub(kl). Specializing anti hsup(A) sub(k) in such a way that they have the form deltasup(A) sub(k) in the preferred coordinates of Minkowski space and using a matter Lagrangian which contains these anti h0sup(A) sub(k) only by the anholonomic components of the metric Christoffel symbols, we obtain a dynamical energy momentum tensor which is equal to the canonical one. Then we consider the relations of the bi-tetrad theory to other theories which are only covariant with respect to global Lorentz transformations from the beginning. As an example we formulate the main relations of the two-component neutrino theory. (author)