Quantum Gravity

by Claus Kiefer

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction -- the direct quantisation of Einstein's general theory of relativity and string theory -- are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility.
This third edition contains new chapters or sections on quantum gravity phenomenology, Horava-Lifshitz quantum gravity, analogue gravity, the holographic principle, and affine quantum gravity. It will present updates on loop quantum cosmology, the LTB model, asymptotic safety, and various discrete approaches. The third edition also contains pedagogical extensions throughout the text.
This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.

Genres: Physics

393 pages, Hardcover

First published August 1, 2004

Reviews

[Nazir · Rating 4 out of 5]

To be frank, I have not read this book cover to cover. So this will be a partial review based off the good chunk that I have read. This monograph is meant to be a summary of the hard problems of quantizing gravity as well as the many proposed ways to do so. On the surface, this book is exactly something you may be interested if you want to have a general perspective on more than one approach to doing quantum gravity (before specializing into something more specific like string theory, loop quantum gravity, etc.). The pre-requisites for this book would be a decent understanding of general relativity (think at the level of Sean Carroll’s textbook), quantum field theory (though not as much as you might think. Knowing the basics of second quantization and the path integral is already good), and just non-relativistic quantum mechanics.

The major positive with this book is that it’s quite easygoing. Mathematical arguments are made in a very loose manner (just like physicists like them), while still capturing the essential physical insights. The first parts of the book deal with perturbative approaches to quantum gravity. In essence covering some of the first attempts at using standard QFT methods to gravity (such as the Gupta-Feynman-DeWitt approach for spin-2 bosons). The book then goes into some aspects of causal sets, the Hamiltonian formalism of general relativity, and some aspects of loop quantum gravity. It then takes a turn to cover areas where quantum gravitational effects are relevant for meaningful physics. Namely quantum black holes and quantum cosmology. The book ends on some brief aspects of developments in string theory, as well as promising phenomenology related to quantum gravity.

While this is a great collection of topic for the generalist, I can imagine it being extremely hard to write a technically thorough account of all of these heavy topics (especially as a sole author). So while it is a great book to get the basic gist of some things, it serves better as a springboard to other things like specialized books or review articles. A really good general review article being Lectures in Quantum Gravity by Ivano Basile et. al. (2025). These covers things like perturbative approaches, asymptotically safe gravity, aspects of string theory, and semiclassical gravity, in far more depth (and a bit more updated).

The book is still definitely worth your time if all I stated above seem to be what you’re looking for. For a book that is equally good, modern, but less mathematically involved, I would also strongly recommend Conversations on Quantum Gravity by Jacome Armas.