On the validity of ADM formulation in 2D quantum gravity

TL;DR

This paper explores the ADM formulation of 2D quantum gravity focusing on the loop length as the key dynamical variable, analyzing its effective action with scalar fields and discussing critical dimension and evolution.

Contribution

It provides an analysis of 2D quantum gravity using the ADM approach with a focus on the loop length variable, offering new insights into its effective action and dynamics.

Findings

Effective action of loop length calculated with scalar fields

Discussion of critical dimension in 2D quantum gravity

Analysis of the time development of the loop length

Abstract

We investigate 2d gravity quantized in the ADM formulation, where only the loop length $l(z)$ is retained as a dynamical variable of the gravitation, in order to get an intuitive physical insight of the theory. The effective action of $l(z)$ is calculated by adding scalar fields of conformal coupling, and the problems of the critical dimension and the time development of $l$ are addressed.