Discrete Lorentzian Quantum Gravity

TL;DR

This paper discusses the development of discrete Lorentzian quantum gravity models, emphasizing background independence and presenting new models based on Lorentzian geometries, with promising results in lower dimensions.

Contribution

Introduces a new class of discrete quantum gravity models based on Lorentzian geometries, advancing the study of non-perturbative quantum gravity.

Findings

Successful formulation of Lorentzian models in 2 and 3 dimensions

Unexpected results indicating promising features of Lorentzian models

Potential for these models to serve as non-trivial quantum gravity theories

Abstract

Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated in a background-independent way. After summarizing the status quo of discrete covariant lattice models for four-dimensional quantum gravity, I describe a new class of discrete gravity models whose starting point is a path integral over Lorentzian (rather than Euclidean) space-time geometries. A number of interesting and unexpected results that have been obtained for these dynamically triangulated models in two and three dimensions make discrete Lorentzian gravity a promising candidate for a non-trivial theory of quantum gravity.