Canonical transformation for stiff matter models in quantum cosmology

TL;DR

This paper develops a canonical transformation approach to address factor ordering ambiguities in quantum cosmology models with stiff matter and a cosmological constant, ensuring consistent quantization.

Contribution

The authors introduce specific coordinate transformations that are proven canonical to eliminate factor ordering ambiguities in the superhamiltonian of these models.

Findings

Successfully remove factor ordering ambiguities

Transformations are proven canonical via symplectic method

Applicable to Friedmann-Robertson-Walker models with stiff matter

Abstract

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.