2D $R^2$ gravity in weak coupling limit

TL;DR

This paper studies two-dimensional R-squared quantum gravity in the weak coupling limit, simplifying the dynamics to quantum mechanics of one degree of freedom and explicitly calculating the two-point Green function.

Contribution

It introduces a reduction of 2D R-squared quantum gravity to a quantum mechanical model and provides an explicit calculation of the Green function in Gaussian approximation.

Findings

Dynamics reduces to quantum mechanics of a single degree of freedom

Explicit two-point Green function calculated in Gaussian approximation

Analysis applicable in the limit of infinite invariant volume

Abstract

2D $R^2$ quantum gravity in infinitely large invariant volume is considered. In weak coupling limit the dynamics is reduced to quantum mechanics of a single degree of freedom. The correspondent two - point Green function is calculated explicitly in Gaussian approximation.