Introduction to Quantum Effects in Gravity

by V. Mukhanov, Sergei Winitzki

This book, first published in 2007, is an introductory textbook on quantum field theory in gravitational backgrounds intended for undergraduate and beginning graduate students in the fields of theoretical astrophysics, cosmology, particle physics, and string theory. The book covers the basic (but essential) material of quantization of fields in an expanding universe and quantum fluctuations in inflationary spacetime. It also contains a detailed explanation of the Casimir, Unruh, and Hawking effects, and introduces the method of effective action used for calculating the back-reaction of quantum systems on a classical external gravitational field. The broad scope of the material covered will provide the reader with a thorough perspective of the subject. Every major result is derived from first principles and thoroughly explained. The book is self-contained and assumes only a basic knowledge of general relativity. Exercises with detailed solutions are provided throughout the book.

Genres: Physics

284 pages, Hardcover

First published June 14, 2007

Reviews

[Erickson · Rating 4 out of 5]

*Second reading*: mainly skimmed through the details from Chapter 1-Chapter 7 for my comprehensive exams. I think I still hold on to my earlier views that this book has very nice intuitive examples using harmonic oscillators and expanding universe. It's extremely helpful to learn from this instead of jumping straight to general relativistic settings. However, it is also true that this book alone will not get you far, and in some cases it did not go deep enough (for example, it mentions nothing about unitary equivalence).

So overall, anyone who reads or studies QFT in curved spacetimes should at least read this book once quickly, at least for Part I. I never really went through Part II, but I believe it will be useful for people who know effective field theory and effective action. I cannot stress how useful the appendices of this book is for beginners.

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Forgot to close the book; I read this as part of coursework taken on QFT for cosmology which is based on this book's first ten chapters. I did not read the rest because I did not need it, and it seemed to rely on path integrals which I never learnt before (which is okay because the course does not deal with interacting QFT).

The book is quite clearly written, and the whole issue of Bogoliubov transformation in QFT that seemed mysterious and complex was skillfully reduced to the analogous problem of driven harmonic oscillator. However, I think the book does lack some important details that are covered in e.g. other texts such as Birrell/Davies, though I believe it's for a good reason. I also found some discussion on cosmological observables and fluctuations unclear; possibly because one is assumed to know basic cosmology before reading, even though it is readable without.

The appendices are surprisingly useful, especially the part about distributions and generalized functions. It conveys the messages clearly.