Comment on the choice of time in a two-component formulation of the Wheeler--DeWitt equation

TL;DR

This paper revisits the two-component formalism in quantum cosmology, focusing on how the choice of time affects the appearance of imaginary eigenvalues, and demonstrates that a proper global time choice avoids this issue.

Contribution

It clarifies the relationship between time choice and eigenvalue properties in the two-component Wheeler--DeWitt formalism, proposing a way to select a suitable global time.

Findings

Proper global time choice prevents imaginary eigenvalues.

The relation between time identification and eigenvalue appearance is established.

The formalism's consistency is improved by appropriate time selection.

Abstract

The two-component formalism in quantum cosmology is revisited with a particular emphasis on the identification of time. Its relation with the appearance of imaginary eigenvalues is established. It is explicitly shown how a good choice of the global time prevents this peculiarity.