A similar conceptual shift occurs between the invariant interval of Einstein's general relativity and the parallel transport of Einstein–Cartan theory.
[5] Particularly, Sen discovered a new way to write down the two constraints of the ADM Hamiltonian formulation of general relativity in terms of these spinorial connections.
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.
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.
Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial.
The kinematics are encoded in the Gauss and Diffeomorphism constraints, whose solution is the space spanned by the spin network basis.
The present version of the covariant dynamics is due to the convergent work of different groups, but it is commonly named after a paper by Jonathan Engle, Roberto Pereira and Carlo Rovelli in 2007–08.
This approach is related to state-sum models of statistical mechanics and topological quantum field theory such as the Turaeev–Viro model of 3D quantum gravity, and also to the Regge calculus approach to calculate the Feynman path integral of general relativity by discretizing spacetime.