METRIC-AFFINE GAUGE-THEORY OF GRAVITY - FIELD-EQUATIONS, NOETHER IDENTITIES, WORLD SPINORS, AND BREAKING OF DILATION INVARIANCE

In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant der ivative of the metric). In the gauging of the general affine group A(4 , R) and of its subgroup GL(4, R) in four dimensions, energy-momentum and hypermomentum currents of matter are canonically coupled to the co frame and to the connection of a metric-affine spacetime with nonvanis hing torsion and nonmetricity, respectively Fermionic matter can be de scribed in this framework by half-integer representations of the <(SL) over bar>(4, R) covering subgroup. We set up a (first-order) Lagrangia n formalism and build up the corresponding Noether machinery. For an a rbitrary gauge Lagrangian, the three gauge field equations come out in a suggestive Yang-Mills like form. The conservation-type differential identities for energy-momentum and hypermomentum and the correspondin g complexes and superpotentials are derived. Limiting cases such as th e Einstein-Cartan theory are discussed. In particular we show, how the A(4, R) may ''break down'' to the Poincare (inhomogeneous Lorentz) gr oup. In this context, we present explicit models for a symmetry breakd own in the cases of the Weyl (or homothetic) group, the SL(4, R), or t he GL(4, R).