Restoring unitarity in anisotropic quantum cosmological models

The present work shows that a properly chosen ordering of operators can restore unitarity in anisotropic quantum cosmological models. Bianch V and Bianchi IX models with a perfect fluid are worked out. It has been shown that a transformation of coordinates takes the Hamiltonian to that of an inverse square potential which has equal deficiency indices and a self-adjoint extension is thus possible. It is also shown, although not detected clearly before, that isotropic models are also apt to violate the conservation of probability for a careless operator ordering.