Time in quantum theory, the Wheeler-DeWitt equation and the Born-Oppenheimer approximation

TL;DR

This paper compares gauge-fixing and Born-Oppenheimer approaches to the Wheeler-DeWitt equation in quantum cosmology, showing they yield similar results in a simple model and discussing the broader problem of time in quantum theories.

Contribution

It provides a comparative analysis of two methods for introducing time in quantum cosmology and explores their implications and similarities in a simplified setting.

Findings

Both approaches produce similar predictions in the tested model.

The paper discusses the problem of time in quantum mechanics.

It examines the classical-quantum correspondence in cosmological contexts.

Abstract

We compare two different approaches to the treatment of the Wheeler-DeWitt equation and the introduction of time in quantum cosmology. One approach is based on the gauge-fixing procedure in theories with first-class constraints, while the other uses the Born-Oppenheimer method. We apply both to a very simple cosmological model and observe that they give similar predictions. We also discuss the problem of time in non-relativistic quantum mechanics and some questions concerning the correspondence between classical and quantum theories.