A new look at loop quantum gravity

TL;DR

This paper reviews recent progress in loop quantum gravity, highlighting a well-defined background-independent framework with explicit transition amplitudes and a simple vertex function, while discussing open challenges.

Contribution

It presents a comprehensive perspective on the current state of loop quantum gravity, emphasizing the development of explicit dynamics and the role of locality and invariance principles.

Findings

A well-defined background-independent kinematics is established.

Explicit computation of transition amplitudes is possible in various regimes.

A simple vertex function encapsulates the dynamics, guided by key invariance principles.

Abstract

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems.