One Local Solution of the Wheeler-DeWitt equation

TL;DR

This paper presents a local solution to the Wheeler-DeWitt equation in quantum gravity, utilizing an up-to-down method that applies broadly to different metric treatments, including the mini-superspace approach.

Contribution

It introduces a novel local solution method for the Wheeler-DeWitt equation based on the up-to-down approach, applicable to general metrics in quantum gravity.

Findings

Successfully obtains a local solution to the Hamiltonian constraint.

Demonstrates the method's applicability to various metric treatments.

Provides insights into the structure of quantum gravity states.

Abstract

We can obtain one solution of the Hamiltonian constraint equation in the local sense. The form of the state is suggested from the up-to-down method in our previous work. The up-to-down method works for different way in treating the general metrics. In the mini-superspace approach there appears additional constraint in the 4-dimensional quantum gravity Hilbert space. However, in the general treatment of the metrics this method works as only solving technique.