Quantum Gravity

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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. Among the approaches include 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. Chapter 1 gives a general introduction into the problem of quantizing the gravitational field. Chapter 2 then presents the main covariant approaches — perturbation theory and Feynman diagrammes, path integrals, and supergravity. Chapter 3 discusses, for simpler systems, the important concept of reparametrization invariance which plays a crucial role in the Hamiltonian formulation of general relativity discussed thereafter. Chapter 5 presents the canonical quantization in the metric variables, leading to the central Wheeler-DeWitt equation, while Chapter 6 presents loop quantum gravity. The next two chapters 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. The book concludes with a discussion of the relevance of quantum gravity for the interpretation of quantum theory.

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