An Approach to Quantum 2D Gravity

TL;DR

This paper develops a model of two-dimensional quantum gravity with quadratic curvature action, utilizing Gaussian measures and Wiener path integrals to compute metric correlations perturbatively.

Contribution

It introduces a novel approach to 2D quantum gravity using SL(2,R) invariant measures and reduces complex path integrals to Wiener integrals for analytical tractability.

Findings

Calculated the first-order metric correlation function.

Established a framework for perturbative analysis of 2D quantum gravity.

Connected path integral formulation with Wiener processes.

Abstract

We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure. We reduce these path integrals to the products of Wiener path integrals and calculate the correlation function of the metric in the first perturbative order.