Canonical Quantum Gravity

TL;DR

This paper reviews the history, approaches, and challenges of canonical quantum gravity, focusing on geometrodynamics and connection dynamics, and discusses the algebraic quantization program and the problem of observables.

Contribution

It provides a comparative overview of classical and quantum canonical gravity, emphasizing visualization and algebraic methods, and highlights unresolved issues like observables.

Findings

Comparison of geometrodynamics and connection dynamics

Discussion of algebraic quantization methods

Analysis of the problem of observables in quantum gravity

Abstract

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical theory as I can by pictorial visualization. Algebraic aspects dominate my description of the quantization program. I address the problem of observables. The reader is encouraged to follow the broad outlines and not worry about the technical details.