Probing Quantum General Relativity Through Exactly Soluble Midi-Superspaces II: Polarized Gowdy Models

Canonical quantization of the polarized Gowdy midi-superspace with a 3-torus spatial topology is carried out. As in an earlier work on the Einstein-Rosen cylindrical waves, symmetry reduction is used to cast the original problem in 4-dimensional space-times to a 3-dimensional setting. To our knowledge, this is the first complete, systematic treatment of the Gowdy model in the geometrodynamical setting.