Quantization of gravity

Establish a mathematically consistent, background-independent quantization of general relativity that respects diffeomorphism invariance and resolves the non-renormalizability encountered in conventional quantum field theoretic treatments of the spacetime metric.

Background

The paper begins by situating its technical results within the broader context of quantum gravity. It emphasizes that diffeomorphism invariance, the absence of a fixed background, and non-renormalizability obstruct a straightforward quantum field theoretic quantization of general relativity. As a consequence, constructing a rigorous quantum theory of the spacetime metric remains a central challenge.

To address aspects of this broader problem, the authors study simplified models—specifically two-dimensional dilaton gravity (Jackiw-Teitelboim) and Bianchi IX minisuperspace quantum cosmology—where path integrals can be handled more tractably, aiming to clarify structural features relevant to quantum gravity.