Introduction

Loop quantum gravity is a non-perturbative approach to the quantum theory of gravity, in which no classical background metric is used. In particular, its starting point is not a linearized theory of gravity. As a consequence, while it still operates according to the rules of quantum field theory, the details are quite different from those for field theories that operate on a fixed classical background space-time. It has considerable successes to its credit, perhaps most notably a quantum theory of spatial geometry, in which quantities such as area and volume are quantized in units of the Planck length, and a calculation of black hole entropy for static and rotating, charged and neutral black holes. But there are also open questions, many of them surrounding the dynamics (“quantum Einstein equations”) of the theory.

In contrast to other approaches such as string theory, loop quantum gravity is rather modest in its aims. It is not attempting a grand unification, and hence is not based on an overarching symmetry principle, or some deep reformulation of the rules of quantum field theory. Rather, the goal is to quantize Einstein gravity in four dimensions. While, as we will explain, a certain amount of unification of the description of matter and gravity is achieved, in fact, the question of whether matter fields must have special properties to be consistently coupled to gravity in the framework of loop quantum gravity is one of the important open questions in loop quantum gravity.