Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics

by Robert M. Wald, Henry J. Frisch (Editor), Gene F. Mazenko (Editor)

In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth.

This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum field theory, and will be of interest to scientists in general relativity and related fields.

Genres: Physics, Science, Mathematics, Philosophy

220 pages, Paperback

First published November 15, 1994

Reviews

[Erickson · Rating 4 out of 5]

Forgot to close the book; I used this as part of reading group session with my colleagues in Spring 2018 on QFT in curved spacetimes. We only managed to read the first five chapters, but I think the remainder is not that much of an issue since the real details in the first five chapters.

This book goes into a more technical aspects of the theory (i.e. not just "putting hats"), and did stuff rigorously (but briefly) though not the level of the modern algebraic QFT (AQFT). Wald focused a lot on scattering theory formalism, and the notion of Hilbert spaces constructed out of the space of solutions of the Klein-Gordon equations. The construction, properly understood, reveals deep insights on why we are even doing canonical quantization the way we are usually taught in standard "particle physics" QFT: the reason has to do with the existence of natural Fourier transform whose eigenbasis is the eigenbasis of the D'Alembertian operator. If one were to pick modern AQFT texts, it would not actually sound the same as how Wald wrote it. But the fact that much of QFTCS can be made this rigorous is satisfying.

I admit that I didn't fully appreciate the textbook yet, so I guess I have to revisit at some point if I have time. There is only one reason why there's a 4-star instead of 5; I found the non-Latex typesetting jarring, especially considering that the book is written fairly late (even Birrell/Davies text has a much better typeset).

[Skymeson Rolnick]

I loved the chapter on Moving Mirrors. This is a great book but probably not the best for comprehension.

[João · Rating 4 out of 5]

This book goes over how to construct a quantum field theory in curved spacetime and then applies this construction to derive the Unruh and the Hawking effects.

The explanations are very clear, but this is a very formal book in the physicist reference frame so it is quite dense and takes a lot of attention to read. It only covers free theories and it also gives an introduction to algebraic QFT as a way to rigorously define QFT in curved spacetime.

If you want to understand the basics of QFT in curved spacetime in a rigorous way, this is the way to go. However, if you're looking to learn techniques to do concrete calculations in research this book won't help much.