The Born-Oppenheimer Method, Quantum Gravity and Matter

TL;DR

This paper explores various implementations of the Born-Oppenheimer method in quantum gravity and matter systems, analyzing their effects on unitarity and comparing different quantization approaches.

Contribution

It compares different quantum gravity-matter approaches using the BO method, highlighting how back reaction and non-adiabatic effects influence unitarity and clarifies distinctions between formulations.

Findings

Including back reaction removes unitarity violations.

A loop space formulation differs from traditional BO approaches.

The loop formulation resembles a non-BO quantization method.

Abstract

We illustrate and examine diverse approaches to the quantum matter-gravity system which refer to the Born-Oppenheimer (BO) method. In particular we first examine a quantum geometrodynamical approach introduced by other authors in a manner analogous to that previously employed by us, so as to include back reaction and non-adiabatic contributions. On including such effects it is seen that the unitarity violating effects previously found disappear. A quantum loop space formulation (based on a hybrid quantisation, polymer for gravitation and canonical for matter) also refers to the BO method. It does not involve the classical limit for gravitation and has a highly peaked initial scalar field state. We point out that it does not resemble in any way to our traditional BO approach. Instead it does resemble an alternative, canonically quantised, non BO approach which we have also previously discussed.