Two-Dimensional Quantum Gravity in Temporal Gauge

TL;DR

This paper introduces a new gauge in 2D quantum gravity, simplifying the system to quantum mechanics of loop length and rederiving the $c=0$ string field theory with a natural pregeometric Hamiltonian.

Contribution

It proposes a novel gauge in 2D quantum gravity and connects it to existing string field theory, providing new insights into the system's structure.

Findings

System reduces to quantum mechanics of loop length

Reproduces the $c=0$ string field theory

Pregeometric form of the Hamiltonian is naturally obtained

Abstract

We propose a new type of gauge in two-dimensional quantum gravity. We investigate pure gravity in this gauge, and find that the system reduces to quantum mechanics of loop length $l$. Furthermore, we rederive the $c\!=\!0$ string field theory which was discovered recently. In particular, the pregeometric form of the Hamiltonian is naturally reproduced.