Further simplification of the constraints of four-dimensional gravity

The super-Hamiltonian of 4-dimensional gravity as simplified by Ashtekar through the use of gauge potential and densitized triad variables can furthermore be succinctly expressed as a Poisson bracket between the volume element and other fundamental gauge-invariant elements of 3-geometry. This observation naturally suggests a reformulation of non-perturbative quantum gravity wherein the Wheeler-DeWitt Equation is identical to the requirement of the vanishing of the corresponding commutator. Moreover, this reformulation singles out spin network states as the preeminent basis for expansion of all physical states.