Semiclassical approximation of the Wheeler-DeWitt equation: arbitrary orders and the question of unitarity

TL;DR

This paper extends a semiclassical approximation scheme for the Wheeler-DeWitt equation to arbitrary orders, investigates unitarity violations, and proposes modifications involving matter back reaction to restore unitarity.

Contribution

It introduces a generalized approximation method for quantum gravity and addresses unitarity issues by incorporating matter back reaction effects.

Findings

Unitarity violation arises in the approximation scheme.

Back reaction from matter can restore unitarity.

The approach relies on gauge aspects from molecular physics.

Abstract

We extend the Born-Oppenheimer type of approximation scheme for the Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this scheme and show that unitarity can be restored by an appropriate modification which requires back reaction from matter onto the gravitational sector. In our analysis, we heavily rely on the gauge aspects of the standard Born-Oppenheimer scheme in molecular physics.