Vacuum Energy Estimates in Quantum Gravity and the Wheeler-DeWitt Equation

TL;DR

This paper develops a gauge fixing scheme within the Wheeler-DeWitt framework to derive a Schrödinger-like equation, enabling quantum corrections calculation in quantum gravity, exemplified by the Schwarzschild wormhole case.

Contribution

It introduces a novel gauge fixing procedure to recover a Schrödinger-type equation in quantum gravity, allowing for quantum correction calculations.

Findings

Derived a Schrödinger-like equation in quantum gravity

Applied the scheme to the Schwarzschild wormhole case

Enabled calculation of quantum corrections to classical quantities

Abstract

In the Wheeler-DeWitt framework, by a gauge fixing procedure, we set up a scheme to recover a Schr\"odinger type equation, living in the orbits space with the {\it lapse} function as evolution parameter. By means of the associated stationary equation, we have the possibility of calculating quantum corrections to classical quantities. The Schwarzschild wormhole case is discussed as an example of application.