Quantization of static space-times

TL;DR

This paper presents a loop quantum gravity approach to quantize static 4D space-times by reducing them to 3D Euclidean gravity coupled with a scalar field, resulting in a finite Hamiltonian operator.

Contribution

It introduces a novel quantization of static space-times via a 3D Euclidean gravity and scalar field model within loop quantum gravity, with a finite Hamiltonian constraint.

Findings

Hamiltonian constraint is a densely defined, finite operator

Kinematical Hilbert space combines gravity and scalar field sectors

Quantized model offers new insights into quantum gravity problems

Abstract

A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum theory which actually describes quantized static space-times. The Kinematical Hilbert space is the product of the Hilbert space of gravity with that of imaginary scalar fields. It turns out that the Hamiltonian constraint of the 2+1 model corresponds to a densely defined operator in the underlying Hilbert space, and hence it is finite without renormalization. As a new point of view, this quantized model might shed some light on a few physical problems concerning quantum gravity.