GRG Editor's Choice: Semiclassical approximation of the Wheeler–DeWitt equation

© SpringerKiefer, C. & Wichmann, D., Semiclassical approximation of the Wheeler–DeWitt equation: arbitrary orders and the question of unitarity, Gen Relativ Gravit (2018) 50: 66.

Editor's Choice (Research Article)

First Online: 21 May 2018

"The authors discuss in detail the origin of the non-unitarity previously found and propose a strategy to recover a unitary evolution at a given order. Unitarity is restored by modifying what the authors call the `gravitational part of the wavefunction', in a way that can be interpreted as accounting for the backreaction of matter on gravity. This is a nice result. The paper is written in a very clear way. The main arguments and calculations are easy to follow, and the physical interpretation is made transparent by using an analogy with the familiar Born–Oppenheimer approximation in molecular physics."


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.

The authors: 

kiefer-wichmann © kiefer-wichmannClaus Kiefer is professor in the Gravitation and Relativity group at the University of Cologne, Germany. David Wichmann earned his MSc at the University of Cologne and is now a PhD candidate at Utrecht University, The Netherlands.

GRG Editor's Choice:

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community.