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Keywords:

  • Canonical quantum gravity.

Abstract

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.