Generalization of Hajicek and Kuchaˇr’s canonical quantization scheme to the 3+1 geometries admitting maximally symmetric two-dimensional surfaces

摘要

The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization Assumption and an accompanying Requirement is put forward, which enables the canonical quantization of these geometries. The resulting Wheeler– deWitt equation is based on a re-normalized manifold parameterized by three smooth scalar functionals and the entire space of solutions to this equation is analytically given.