a full clear systematic theory and particularly failed to clearly discuss the conjugate momenta to the spinorial variables, its physical interpretation, and its relation to the metric (in his work he indicated this as some lambda variable). In 1986–87, physicist Abhay Ashtekar completed the project which Amitabha Sen began. He clearly identified the fundamental conjugate variables of spinorial gravity: The configuration variable is as a spinoral connection (a rule for parallel transport; technically, a connection) and the conjugate momentum variable is a coordinate frame (called a vierbein) at each point.Abhay Ashtekar, "New Hamiltonian formulation of general relativity," Phys. Rev. D36, 1587-1602, 1987. So these variable became what we know as Ashtekar variables, a particular flavor of Einstein–Cartan theory with a complex connection. General relativity theory expressed in this way, made possible to pursue quantization of it using well-known techniques from quantum gauge field theory. The quantization of gravity in the Ashtekar formulation was based on Wilson loops, a technique developed by Kenneth G. Wilson in 1974 to study the strong-interaction regime of quantum chromodynamics (QCD). It is interesting in this connection that Wilson loops were known to be ill-behaved in the case of standard quantum field theory on (flat) Minkowski space, and so did not provide a nonperturbative quantization of QCD. However, because the Ashtekar formulation was background-independent, it was possible to use Wilson loops as the basis for nonperturbative quantization of gravity. Due to efforts by Sen and Ashtekar, a setting in which the Wheeler–DeWitt equation was written in terms of a well-defined Hamiltonian operator on a well-defined Hilbert space was obtained. This led to the construction of the first known exact solution, the so-called Chern–Simons form or Kodama state. The physical interpretation of this state remains obscure. In 1988–90, Carlo Rovelli and Lee Smolin obtained an explicit basis of states of quantum geometry, which turned out to be labeled by Penrose's spin networks.Carlo Rovelli and Lee Smolin, "Loop space representation of quantum general relativity," Nuclear Physics B331 (1990) 80-152. In this context, spin networks arose as a generalization of Wilson loops necessary to deal with mutually intersecting loops. Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial. Loop quantum gravity (LQG) thus became related to topological quantum field theory and group representation theory. In 1994, Rovelli and Smolin showed that the quantum operators of the