Speaker
Description
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. The canonical Loop Quantum Gravity approach, the spiritual successor of Quantum Geometrodynamics, resolved these problems at the expense of introducing a few aesthetically displeasing features. These include non--separable Hilbert spaces, non--strongly continuous representations and states that are excited on very singular geometries. In this talk, we propose a novel approach to overcome the difficulties faced by Quantum Geometrodynamics, while avoiding the above-mentioned characteristics of canonical Loop Quantum Gravity. We employ a lattice discretization that adheres as closely as possible to the original formulation, and examine the lattice corrections to the theory. We discuss the steps necessary for obtaining a well--defined continuum limit and explain how to perform calculations in the effective theory. The accompanying talk, titled "Reviving Quantum Geometrodynamics: Representations of the Kinematical Observables and the Diffeomorphism Group," will delve further into the intricacies of our approach.
