Gravity quantized

TL;DR

This paper constructs a quantum gravity model by applying loop quantum gravity to gravity coupled to a massless scalar field, using relational Dirac observables and deparametrization with the scalar as internal time. It develops the classical and quantum structure, identifying the necessary Hilbert spaces, operators, and Dirac observables, and then implements these within LQG to build a diffeomorphism-invariant framework with a well-defined physical Hamiltonian. The approach preserves the full local degrees of freedom and provides a route to studying quantum spacetime effects in cosmology and black hole physics, while acknowledging ambiguities in the scalar constraint operator. The work also clarifies its relation to Brown-Kuchar reduced-phase-space quantization, showing how the present scheme builds the physical Hilbert space directly in the full theory rather than via classical reduction.

Abstract

..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consist of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except for that it involves all the local degrees of freedom because no symmetry reduction has been performed at the classical level.