Canonical Quantization of Non-Einsteinian Gravity and the Problem of Time

TL;DR

This paper explores various approaches to quantizing a 1+1 dimensional gravity theory with torsion, demonstrating their equivalence and discussing fundamental issues like the problem of time in quantum gravity.

Contribution

It introduces multiple methods for formulating quantum gravity in a simplified 1+1 dimensional model and shows their consistency, addressing key conceptual challenges.

Findings

Different quantization approaches yield the same finite-dimensional quantum system

The framework provides insights into the problem of time in quantum gravity

The methods unify various formulations of quantum gravity in lower dimensions

Abstract

For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity like e.g.\ the problem of time are discussed in this framework.