Quantization of static space-times

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.

14 pages, made a few modifications, added Journal-ref

References in corpus (3)

• Absence of Singularity in Loop Quantum Cosmology
• A finiteness proof for the Lorentzian state sum spinfoam model for quantum general relativity
• Statistical geometry of random weave states

Cited by in corpus (3)

• Fundamental Structure of Loop Quantum Gravity
• Loop quantum cosmology in 2+1 dimension
• 2+1 dimensional loop quantum cosmology of Bianchi I models