Restoring unitarity in anisotropic quantum cosmological models

TL;DR

This paper demonstrates that appropriate operator ordering can restore unitarity in anisotropic quantum cosmological models, including Bianchi V and IX, by transforming the Hamiltonian into an inverse square potential with self-adjoint extensions.

Contribution

It introduces a method of operator ordering that ensures unitarity in anisotropic quantum cosmological models, addressing previous issues with probability conservation.

Findings

Proper operator ordering restores unitarity in Bianchi V and IX models.

Transformation to inverse square potential allows self-adjoint extensions.

Isotropic models may also violate probability conservation with careless ordering.

Abstract

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.