Metricaffine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance
Abstract
In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group A(4, R) and of its subgroup GL(4, R) in four dimensions, energymomentum and hypermomentum currents of matter are canonically coupled to the coframe and to the connection of a metricaffine spacetime with nonvanishing torsion and nonmetricity, respectively. Fermionic matter can be described in this framework by halfinteger representations of the overlineSL(4, R) covering subgroup. We set up a (firstorder) Lagrangian formalism and build up the corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three gauge field equations come out in a suggestive YangMills like form. The conservationtype differential identities for energymomentum and hypermomentum and the corresponding complexes and superpotentials are derived. Limiting cases such as the EinsteinCartan theory are discussed. In particular we show, how the A(4, R) may “break down” to the Poincaré (inhomogeneous Lorentz) group. In this context, we present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the SL(4, R), or the GL(4, R).
 Publication:

Physics Reports
 Pub Date:
 July 1995
 DOI:
 10.1016/03701573(94)00111F
 arXiv:
 arXiv:grqc/9402012
 Bibcode:
 1995PhR...258....1H
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 197 pages