Factor ordering in standard quantum cosmology

TL;DR

This paper investigates how different factor orderings in the Wheeler-DeWitt equation affect the quantum cosmological models, revealing that the choice of ordering influences the critical energy and the behavior of the wave function.

Contribution

It introduces a formulation of the Wheeler-DeWitt equation with arbitrary factor ordering and analyzes its impact on the model's properties and probability interpretation.

Findings

Wave function behavior depends on matter field energy and factor ordering.

Certain orderings can eliminate the critical energy threshold.

A scalar product enables probability interpretation in quantum cosmology.

Abstract

The Wheeler-DeWitt equation of Friedmann models with a massless quantum field is formulated with arbitrary factor ordering of the Hamiltonian constraint operator. A scalar product of wave functions is constructed, giving rise to a probability interpretation and making comparison with the classical solution possible. In general the bahaviour of the wave function of the model depends on a critical energy of the matter field, which, in turn, depends on the chosen factor ordering. By certain choices of the ordering the critical energy can be pushed down to zero.