Theory of Relativity (2nd Edition) to regard the connection as the basic field and the metric merely as a derived concept. Consequently, the primordial action in four dimensions should be constructed from a metric-free topological action such as the Pontryagin invariant of the corresponding gauge connection. Similarly as in the Yang–Mills theory, a quantization can be achieved by amending the definition of curvature and the Bianchi identities via topological ghosts. In such a graded Cartan formalism, the nilpotency of the ghost operators is on par with the Poincaré lemma for the exterior derivative. Using a BRST antifield formalism with a duality gauge fixing, a consistent quantization in spaces of double dual curvature is obtained. The constraint imposes instanton type solutions on the curvature-squared 'Yang-Mielke theory' of gravity, proposed in its affine form already by Weyl 1919 and by Yang in 1974. However, these exact solutions exhibit a 'vacuum degeneracy'. One needs to modify the double duality of the curvature via scale breaking terms, in order to retain Einstein's equations with an induced cosmological constant of partially topological origin as the unique macroscopic 'background'. Such scale breaking terms arise more naturally in a constraint formalism, the so-called BF scheme, in which the gauge curvature is denoted by F. In the case of gravity, it departs from the meta-linear group SL(5, R) in four dimensions, thus generalizing (Anti-)de Sitter gauge theories of gravity. After applying spontaneous symmetry breaking to the corresponding topological BF theory, again Einstein spaces emerge with a tiny cosmological constant related to the scale of symmetry breaking. Here the 'background' metric is induced via a Higgs-like mechanism. The finiteness of such a deformed topological scheme may convert into asymptotic safeness after quantization of the spontaneously broken model. See also Mathematics of general relativity Hamilton–Jacobi–Einstein equation (HJEE) Numerical relativity Black hole electron References This Ph.D. thesis offers a readable account of the long development of the notion of "geometrodynamics". This book focuses on the philosophical motivations and implications of the modern geometrodynamics program. See chapter 43 for superspace and chapter 44 for spacetime foam. online version (subscription required) J. Wheeler (1960) "Curved empty space as the building material of the physical world: an assessment", in Ernest Nagel (1962) Logic, Methodology, and Philosophy of Science, Stanford University Press. online version (subscription required) online version (subscription required) Mielke, Eckehard W. (2010, July 15). Einsteinian gravity from a topological action. SciTopics. Retrieved January