Quantum Fields in Curved Space

Cambridge Monographs on Mathematical Physics

by N.D. Birrell, Paul C.W. Davies

This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

Genres: Physics, Textbooks, Nonfiction, Science

352 pages, Kindle Edition

First published February 25, 1982

Reviews

[Tomy · Rating 5 out of 5]

El libro es una recopilación de estudios de finales del siglo pasado del intento más modesto de cuantizar la gravedad, en el que el espacio-tiempo es un andamiaje donde las partículas se mueven e interactúan y no se ve perturbado por la propia presencia de las mismas partículas. Parte de las teorías cuánticas de campos en espacio-tiempos planos, que ya son conocidas para cualquier estudiante de teórica de últimos años de la carrera, generalizándolas a los sistemas con presencia de gravedad en los que el espacio-tiempo es curvo. La introducción responde bastante bien a la pregunta de por qué la gravedad es tan difícil de cuantizar con respecto al resto de interacciones.

Así, los autores estudian en profundidad la generación de partículas en espacio-tiempos no inerciales: el efecto Unruh en observadores acelerados, la radiación Hawking en el colapso gravitatorio de una estrella a un agujero negro y la creación de partículas por la expansión del Universo. Si la Relatividad tiró por tierra la concepción universal de espacio y tiempo, esta teoría tira la concepción universal de partícula, ya que unos observadores detectarán partículas mientras que otros no, por lo tanto, ¿qué es la materia?

También dedican un capítulo extenso a “sanar” las teorías cuánticas de campos a través de la renormalización. Que se resume en quitarte infinitos restando infinitos con cierto flow para que las teorías no den resultados raros. No le he prestado la misma atención que a otros capítulos pero seguro que es útil para resolver las ecuaciones de Einstein en regiones semiclásicas-semicuánticas.

Recomiendo el libro encarecidamente para meterse en el tema de la gravedad cuántica y empezar a entender las tensiones conceptuales a las que se enfrenta parte de la comunidad. Quizá, para continuar con una guía de estudio recomendaría abordar el lenguaje de tetradas de la Relatividad General, el formalismo hamiltoniano de RG y la cuantización para sistemas con ligaduras desarrollada por Dirac.

[Erickson · Rating 3 out of 5]

Finished first five chapters (which is what I needed for comprehensive exams) and also I had read Chapter 8 as part of my own research.

Overall, I cannot say that I learnt very useful things from this book, from the perspective of a "student". It's too old, possibly outdated, and as a monograph it's more like a collection of results which are rather difficult to follow. However, it certainly did well -as a monograph- in serving as a reference text on what has been done or can be done in the field. In fact, my first impression was that the book covered all there is to cover for this field, and there's probably nothing much left to be investigated. I should also say that Chapter 2, first three sections of Chapter 3, and Chapter 8 are actually really nice.

What follows is probably personal opinion that depends strongly on my own abilities (which may not be the same for everyone). I find the exposition about adiabatic vacuum very confusing in Chapter 3, so much so that it did not help me clarify conceptually why it's as important as conformal vacuum or any other vacuum. I get the motivations but I doubt I got any working knowledge out of it. The cosmological spacetime examples (including de Sitter) were helpful, but they were helpful insofar as you have easy access to solutions of highly non-trivial differential equations (I have Mathematica so it's fine). So I don't know if I would rate this book as great; I think it's not worth 4-star, but there's no 3.5 star so I would lean on giving 3 than 4.

There are more modern resources; Parker and Tom's book is particularly nice (from what I heard). However, for the stuff I needed, Tom and Parker did not cover much as they focused much on stress-energy tensors and renormalization. I seriously think this field --- QFT in curved spacetimes --- need better pedagogical textbooks. Mukhanov did a very good job actually (contrary to what I heard from others), but it's true that Mukhanov's textbook somehow left you with the sense that you understand some of the basic features really well but yet you don't really know anything more than the -very- bare basics. Ironically, the more -algebraic- oriented stuff, like those in algebraic QFT (AQFT), are better at the story-telling, and I wished there's something similar for this kind...

[João · Rating 3 out of 5]

This is the go-to book to learn about QFT in curved spacetime. It covers just about anything you might need to use in actual research. The explanations are quite clear and they go over many explicit examples in a lot of detail so it's a great reference to learn how to compute things.

The main disadvantage of this book is that it is quite outdated in places. It's view of renormalisation is very much based on cancelling infinities rather than Wilsonian RG. Also, it doesn't mention inflation at all. Which is a shame given a lot of contemporary research on QFT in curved spacetime is motivated by inflation.The physics in chapters 4 and 5 is also quite uninteresting (at least from my point of view), however, some techniques developed here are used later on, so they can't be skipped.

Their discussion of particle detectors is brilliant, very physically motivated and really helps the reader in believing in these phenomena. Chapter 6 on calculating the stress tensor and chapter 9 on dealing with interactions are also unparalleled in terms of clarity of explanation and attention to detail which make them essential for someone who wishes to perform these kinds of computations in practice.

[Ishfaaq Peerally · Rating 3 out of 5]

I was reading it as a recommendation to write my dissertation on blackhole thermodynamics. It is hard, however, if you have no prior knowledge of the fundamentals of QFT in flat space time.

[Brian Powell · Rating 5 out of 5]

The canonical text on the subject from the early days, it remains a solid reference covering the essential topics. In contrast to other treatments (like Wald and Fulling), this text is *practical*; as in, you can use it to do actual calculations. The tone and clarity is variable, though. For example, chapters 4 and 5 on flat and curved space examples of QFT phenomena are engaging and quite clear, whereas chapter 6 and 7 on stress tensor renormalization were essentially incomprehensible to me. As an older text, Birrell and Davies also does not cover the rich application of QFT in curved space to inflationary perturbations. This text, complemented by Parker and Toms (who cover inflationary perturbations and provide much clearer coverage of stress tensor renormalization), should cover all the practical angles and provide a thorough treatment of the subject.

[albin james · Rating 5 out of 5]

his embrace, a fortress
it fuels me
and places
a skeleton of trust
right beneath us
bone by bone
stone by stone
if you ask yourself patiently and carefully:
who is it ?
who is it that never lets you down ?
who is it that gave you back your crown ?
and the ornaments are going around
now they're handing it over
handing it over

he demands a closeness
we all have earned a lightness
carry my joy on the left
carry my pain on the right

if you ask yourself patiently and carefully:
who is it ?
who is it that never lets you down ?
who is it that gave you back your crown ?
and the ornaments are going around
now they're handing it over
handing it over

- Björk