Time and a physical Hamiltonian for quantum gravity

TL;DR

A nonperturbative quantization of general relativity coupled to dust, leading to a physical Hamiltonian with spatial diffeomorphism symmetry that provides a complete theory of quantum gravity and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach.

Abstract

We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts in technical reach applications to cosmology, quantum gravitational collapse and Hawking radiation.