Background independent quantum gravity: a status report

TLDR

Loop quantum gravity can be approached in multiple ways, and this review offers an introductory, non‑exhaustive overview to avoid overwhelming non‑experts. The review aims to introduce loop quantum gravity as a background‑independent, non‑perturbative unification of general relativity and quantum physics, providing a bird’s‑eye view of its current status. It is presented pedagogically, assuming only basic general relativity, gauge theory, and quantum field theory, and focuses on conveying core ideas and results rather than detailed derivations. The review summarizes the present state of the field and serves as a gateway for newcomers to explore loop quantum gravity in depth. References for further reading are listed in the cited bibliography.

Abstract

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.