×

Metric-affine gauge theory of gravity. I: Fundamental structure and field equations. (English) Zbl 0938.83021

From the text: The authors give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric-affine gravity. The results are put into the dynamical framework of a classical field theory. They derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of translations is explained in detail.
Contents: Introduction; Ch. 1. Reference frames and gauge systems illustrated by means of \(\text{SU}(N)\)-Yang-Mills theory (The gauging of \(\text{SU}(N)\), field strengths and Lagrangian). Ch. 2. Gauging the affine group (Affine geometry, Affine frames and physical fields, The gauge procedure, The breaking of translational invariance, Diffeomorphism invariance and Lie derivatives, Anholonomic frames, Introducing a metric: Orthonormal frames). Ch. 3. Metric-affine gravity as a classical field theory (Lagrangian formulation, General model building, Field equations, Noether identities, Subcases of MAG by reducing the affine group). Ch. 4. Pure translation invariance and the reduction from MAG to teleparallelism and GR (Motivation, Einsteinian teleparallelism: Translation gauge potential and Lagrangian, Transition to GR); References.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
PDFBibTeX XMLCite
Full Text: DOI arXiv