Quantum Fields in Curved Space (Cambridge Monographs on Mathematical Physics)

Funny, we're taught that Hawking radiation from a blackhole shows that the blackhole is evaporating. But, the same results can be found using the Unruh effect, if you use the gravitation of the blackhole as the acceleration. All well and good. However, the Unruh effect can occur in a vacuum, and nobody talks about the vacuum evaporating. So,does Hawking radiation really have anything to do with evaporation?

I am a retired physicist, reading this for self study. I have a background in QFT and GR, which of course helps a great deal. Still, this book has enough introductory material that one is led fairly easily to a good understanding of semiclassical effects of quantization in curved spacetime. I would recommend it to any physicist wanted to become familiar with Hawking radiation, the effects of the expansion of the universe on fields and particles, etc.

At the time of publication of this book, there was growing interest in how to formulate quantum field theory in spactimes with curved metrics with the intent of studying to what extent a non-flat curvature would change the properties and behavior of quantum fields as compared to the Minkowski case.The authors give an introduction to this research and they do a good job in that regard. Due to the influence of superstring and M-theory on high energy physics at the present time, fewer researchers are studying the problems as they are cast in this book. On the other hand, interest in the Casimir effect and the behavior of quantum fields at boundaries is still very much alive. This book could still be use to motivate this research. It is expected that anyone reading this book will have a background in quantum field theory in flat space, but one could still perhaps read it without such a background.Quantum field theory in flat spacetime is difficult enough, and it is still not entirely understood from a mathematical perspective. Even the physics of interacting quantum fields is still poorly understood in flat spacetime, especially in its ability to predict a bound state. Therefore, it might seem a bit disconcerting to some for researchers to add further complications to quantum field theory by casting them in curved backgrounds. However, cosmological and astrophysical interests drives this research, as well as more practical considerations arising from the Casimir effect.The renormalization procedures in quantum field theory are further complicated in curved spacetime via the "trace" or "conformal" anomalies. The reader gets a good dose of these in the book in the discussion on the renormalization of the stress. The idea of an "effective" action, which has been exploited with zeal in the flat spacetime case, appears here also.The most important thing to carry away from this book is that the idea of a particle in curved space quantum field theory is not very well-formulated, i.e. particle detectors in such situations are not related to the quantity of matter present in a region as they are in the flat-space case. Doing quantum field theory when gravity is present has instigated a huge amount of research, related to the still unsolved problem of just how to quantize the gravitational field.

Of Stephen W. Hawking, read:"... his study of quantum black holes and the discovery of their thermal emission is a cornerstone of this book."I take this opportunity to lament the passing, and honor the legacy of,Stephen W. Hawking (8 January 1942--14 March 2018)Appropriate it is that Cambridge University Press brought forth this publication nearly ten years after that classic treatise by Hawking and Ellis.Appropriate it is that two exceptional Cambridge University Press publications, Nonequilibrium Quantum Field Theory (2008, Calzetta and Hu) and Quantum Field Theory in Curved SpaceTime (2009, Parker and Toms),refer to this book by Birrell and Davies. It is, and remains, a classic.(1) If you are familiar with Physicist Paul Davies, you already know that his writing style is exemplary. This monograph is no exception. While the content is technical, the physical explanations are lucidly expounded. Indeed, the Preface: "The treatment is intended to be both pedagogical and archival." On both scores, a goal admirably achieved.(2) If perusing the book, keep in mind: the conventions for metric are opposite (+,-,-,-) to Misner, Thorne, Wheeler (-,+,+,+). The paperback printing (1984) has corrections and a brief update to the preface regards interacting fields. This book has a rich (ten page) Reference list, an invaluable asset. Prerequisites to the book are an acquaintance with Track One of MTW and the simpler aspects of Bjorken and Drell.(3) What do we find here ? " An exhaustive account of regularization and renormalization techniques." This is chapter six, an invaluable asset ! Read: "...only in exceptional circumstances does the particle concept in curved space quantum field theory correspond closely to the intuitive physical picture of a subatomic particle." (page 150). That is a point which is re-visited time and time again in this monograph. Of course, this a point which is also emphasized in Wald's 1994 text, Quantum Field Theory in Curved SpaceTime and Black Hole Thermodynamics (see, page 60).(4) The exceptional Sixth Chapter is preceded by the exceptional Third Chapter: "...the high-frequency behavior of the field is independent of the quantum state or the global structure of the spacetime, and depends purely on the local geometry." (page 36). An interesting aside introduces the tetrad (or, vierbein) formalism (page 83).(5) Pedagogic features: Thermal and Conformal relationships between various spacetimes (page 141). An interesting discussion regards Feynman path integral and Schwinger variational principle (page 155), learn that: " Path-integral quantization still works in curved spacetime." At various points in the discussion, we meet topological considerations (including Casimir effect, page 88 and 100). We read: " Energy is a source of gravity and will bring about the very spacetime curvature whose effects we are trying to study. It simply cannot be thrown away, we are not free to rescale the zero-point of energy." (page 152).(6) Regards technicalities: Utilize Bogoliubov transformations, Green's functions, analytic continuation, zeta-function regularization, Fock space and LSZ. It is emphasized that "this instability is not due to different definitions of positive frequency, but rather to the lack of Poincare invariance in curved spacetime." (page 296). Paul Roman's interesting text of Introductory Quantum Field Theory (1969, Wiley) is referenced. Finally, read: "The combined effect of topology, nonzero temperature and curvature on theories involving spontaneously broken symmetries is likely to have been of considerable importance in the early stages of the evolution of the universe." (page 321).(7) In conclusion: This is an exceptionally pedagogic text. It is well-written. It is both introductory and advanced.The monograph has been cited more than eight-thousand times, this, for good reason: it is still relevant !Highly recommended as a rich source of insight and inspiration (as, too, Hawking and Ellis).

One of the better books on quantum fields that I have read so far. An especially good treatment of the Casimir effect and boudary terms is given. The authors have a wonderfully conversive manner of discourse which I enjoyed very much.

The physics content of this book is very good. Unfortunately in the Kindle edition, the reproduction of the equations is poor. The symbols are not sharp, and many of them are too small to read.