A Comparison of Two Quantization Procedures for Lineal Gravity

TL;DR

This paper compares two different quantization methods for 1+1 dimensional gravity, demonstrating that their resulting wave functionals are equivalent, thus providing insight into the consistency of different approaches.

Contribution

It provides a direct comparison of gauge-theoretic and geometric quantization procedures in 1+1 gravity, establishing their equivalence.

Findings

Wave functionals from both approaches are equivalent.

The comparison clarifies the relationship between different quantization methods.

Supports the consistency of various quantization procedures for gravity in low dimensions.

Abstract

We consider two programs for quantizing gravity in $1+1$ dimensions, which have appeared in the literature: one using a gauge--theoretic approach and the other following a more conventional ``geometric'' approach. We compare the wave functionals produced by the two different programs by finding matrix elements between the variables of the two theories. We find that the wave functionals are equivalent.