GL(n,IR), tetrads and generalized space-time dynamics

We discuss the possibility of eliminating the concepts of internal scale and internal geometry from generally-covariant field theories. By internatl scale and internal geometry we mean objects like scalar products, norms, etc, introduced by hand, as primary entities, to internal spaces of field multiplets. Typical examples are: Minkowskian metric in the internal space of gravitational co-tetrad, two-dimensional symplectic form used in spinor theory, and Hermitian or Euclidean scalar products in internal spaces of gauge models. We suggest dynamical models free of such absolute objects, thereby, invariant under full linear groups, not only under 'rigid' subgroups preserving bilinear forms. In particular, constructed are generally-covariant Lagrangians for tetrads invariant under GL(4,R), and Lagrangians for the Weyl spinor - tetrad, invariant under the homomorphically correlated actions of GL(2,C) and the linear Lorentz-conformal group CO(1,3)=R+SO(1,3); the tetrad part is then separately invariant under GL(4,R). In usual models, gravitational Lagrangians are built in a SO(1,3)-invariant way, and Lagrangians for spinor-tetrad systems are invariant under the homomorphically correlated action of SL(2,C) and SO(1,3); dilatations are not symmetries. Discussed are perspectives of physical applications of our models. We also suggest some mechanism of deriving absolute objects like structure constants of gauge groups and spatio-temporal fibration of Kaluza worlds from dynamical principles, e.g. from GL(/n,R)-invariant and generally-covariant Lagrangians for the field of linear frames. (orig.)