Discrete approaches to quantum gravity in four dimensions

TL;DR

This paper reviews three main discrete approaches to formulating a consistent quantum gravity theory in four dimensions, focusing on gauge theories, Regge calculus, and dynamical triangulations.

Contribution

It provides a comprehensive overview of the three major discrete methods for quantum gravity in four dimensions, highlighting their key features and research status.

Findings

Survey of gauge-theoretic approaches in quantum gravity

Analysis of quantum Regge calculus developments

Overview of dynamical triangulations research in four dimensions

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.