Reviving Quantum Geometrodynamics: Susanne Schander (Perimeter Institute) and Thorsten Lang

The Quantum Geometrodynamics program was an early effort to canonically quantize General Relativity in the most straightforward manner possible. The approach involves a formal $3+1$–split of spacetime and applies Dirac’s procedure for the quantization of constraint systems to the ADM formulation of General Relativity, with the configuration variables represented by the components of the spatial metric. While DeWitt was able to write down a formal Hamiltonian constraint operator, the problems of obtaining a well-defined Hilbert space and defining the constraints thereon remained unsurmountable challenges, among others.