Canonical quantization of some midi-superspace models in 2+1 and 3+1 dimensions
AuthorChristodoulakis, T.; Doulis, G.; Terzis, P. A.; Melas, E.; Grammenos, Th; Papadopoulos, G. O.; Spanou, A.
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. © 2009 IOP Publishing Ltd.