A New Model for Quantum Space in Diagrammatic Loop Quantum Gravity

Abstract

In loop quantum gravity space is assumed to consist of finite-size building blocks. Spin networks are used to model this microscopic structure of space. The goal is to create spin networks that have the properties of classical space as it is described by general relativity. Currently this is not possible. This thesis introduces a model such that it is possible to construct spin networks that have the properties of a classical metric. It uses spin networks with 6-valent nodes in a cubic structure and all links have spin 1. This choice is based on the interpretation of the volume operator of loop quantum gravity as the creation operator for volume. A new set of operators is defined that measure length, area and volume in a spin network. Spin networks are constructed for flat space, the Schwarzschild metric and for plane gravitational waves. The first part of this thesis describes a diagrammatic version of loop quantum gravity, where wave functions are represented by diagrams and operators have a graphical action on these diagrams. The interpretation of the volume operator as a creation operator is based on its graphical form.