Causal random geometry from stochastic quantization

TL;DR

This paper reviews a new formulation of 2D causal quantum gravity using Causal Dynamical Triangulations and stochastic quantization, allowing nonperturbative analysis and linking stochastic time to proper time on geometries.

Contribution

It introduces a novel approach combining stochastic quantization with Causal Dynamical Triangulations to derive the quantum Hamiltonian including topology changes.

Findings

Derived the nonperturbative quantum Hamiltonian for 2D causal quantum gravity.

Linked stochastic time to proper time on the geometries.

Enabled sum over topologies in the quantum gravity model.

Abstract

In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including the sum over topologies. Interestingly, the generally fictitious stochastic time corresponds to proper time on the geometries.