# Discrete Approaches to Quantum Gravity

in Four Dimensions

**Renate Loll
**

Max-Planck-Institut für Gravitationsphysik

Am Mühlenberg 1

14476 Potsdam

Germany

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Abstract

The construction of a consistent theory of quantum gravity is a problem in theoretical physics
that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial
quantum theory proceeds via a discretization of space-time and the Einstein action. I review
here three major areas of research: gauge-theoretic approaches, both in a path-integral and a
Hamiltonian formulation; quantum Regge calculus; and the method of dynamical triangulations,
confining attention to work that is strictly four-dimensional, strictly discrete, and strictly
quantum in nature.