# Quantum Gravity: Third Edition

## Claus Kiefer

### Abstract

This book is concerned with the attempts to unify Einstein's theory of general relativity and quantum theory into a theory of quantum gravity. It presents, for the first time, most of the approaches in a single textbook. Among them are canonical quantum gravity (including loop quantum gravity), covariant quantum gravity, and string theory. The book also discusses the relevance of these theories for cosmology and the physics of black holes. The first chapter gives a general introduction to the problem of quantizing the gravitational field. The second chapter then presents the main covariant app ... More

This book is concerned with the attempts to unify Einstein's theory of general relativity and quantum theory into a theory of quantum gravity. It presents, for the first time, most of the approaches in a single textbook. Among them are canonical quantum gravity (including loop quantum gravity), covariant quantum gravity, and string theory. The book also discusses the relevance of these theories for cosmology and the physics of black holes. The first chapter gives a general introduction to the problem of quantizing the gravitational field. The second chapter then presents the main covariant approaches - perturbation theory and Feynman diagrammes, path integrals, and supergravity. The third chapter discusses the important concept of reparametrization invariance in the framework of simple systems: particle models, bosonic string, and parametrized field theory. This concept plays a crucial role in the Hamiltonian formulation of general relativity, which is the topic of Chapter 4. Chapter 5 presents the canonical quantization in the metric variables, leading to the central Wheeler-DeWitt equation, while the sixth chapter presents loop quantum gravity. The next two chapters 7 and 8 then discuss the major applications - quantization of black holes and quantum cosmology. Chapter 9 gives an introduction to string theory by focusing on its quantum gravitational aspects. Chapter 10 contains a discussion of interpretational issues: the relevance of quantum gravity for the foundations of quantum theory and the arrow of time. It also contains a brief review of quantum-gravity phenomenology. The emphasis throughout is on conceptual and formal clarity. Wherever possible, connections between the various approaches are examined.

*Keywords: *
Quantum gravity,
string theory,
loop quantum gravity,
Wheeler-DeWitt equation,
quantum cosmology,
black holes,
Hawking radiation foundations of quantum theory

### Bibliographic Information

Print publication date: 2012 |
Print ISBN-13: 9780199585205 |

Published to Oxford Scholarship Online: May 2012 |
DOI:10.1093/acprof:oso/9780199585205.001.0001 |

### Authors

#### Affiliations are at time of print publication.

Claus Kiefer, *author*

Institute for Theoretical Physics, University of Cologne, Germany

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