Canonical quantization of some midi-superspace models in 2+1 and 3+1 dimensions

Physics

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Scientific paper

A proposal is put forward which enables the canonical quantization of a family of axially symmetric geometries in 2+1 dimensions and a corresponding spherically symmetric family in 3+1 dimensions. The proposal consists of a particular renormalization assumption and an accompanying requirement and results in a Wheeler-DeWitt equation which is based on a renormalized manifold parametrized by three smooth scalar functionals. The aforementioned equation is analytically solved for both the 2+1 and 3+1 case.

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