Transfer Matrix Formalism for Two-Dimensional Quantum Gravity and Fractal Structures of Space-time

TL;DR

This paper introduces a transfer matrix approach to two-dimensional quantum gravity, deriving a Hamiltonian formalism where geodesic distance acts as time, and reveals universal fractal structures in the continuum limit.

Contribution

It develops a novel transfer matrix formalism for 2D quantum gravity and derives a universal function describing its fractal geometry.

Findings

Universal function characterizing fractal structures

Hamiltonian formalism with geodesic distance as time

Continuum limit analysis of 2D quantum gravity

Abstract

We develop a transfer matrix formalism for two-dimensional pure gravity. By taking the continuum limit, we obtain a "Hamiltonian formalism'' in which the geodesic distance plays the role of time. Applying this formalism, we obtain a universal function which describes the fractal structures of two dimensional quantum gravity in the continuum limit.