“Introduction to Quantum Effects in Gravity” by Mukhanov and Winitzki is a book that I spent a significant amount of time reading pretty carefully. I wanted to say a few words about this book. It introduces quantum field theory very carefully, quantizing a massive scalar field in empty space, then going on to do it in certain space times. It shows how to find the vacuum state and introduces Bogoliubov transformations of that state as excited states. From the coefficients of these transformations come the intensity of particles produced of different wavelengths. Detailed calculations are done for the Unruh Effect (which I will talk about in the next post) and Hawking Radiation.
What’s nice about this introduction is how self contained it is. Bogoliubov transformations are introduced early, well motivated, and used throughout the entire book to explain many different phenomena. The particle interpretation of quantum field theory is made pretty clear, with particle densities of certain frequencies related to Bogoliubov coefficients.
For this reason I recommend this book to anyone interested in introducing themselves to the subject.
Interestingly, the presentation of the book demonstrates how little background you need to understand the basics of pretty deep physics. I often hear people worry about specialization in the sciences. Perhaps physics is getting “too deep” and it takes so long for physicists to learn about one little subject, upon which a mountain of research has been done, that they become unable to effectively do their job. I think this fear is a little misplaced. While it is definitely true that the gestation time for a physicist is very long, the more research is done on a subject, the better it is understood within the context of all other physics, and the better taught it is. It takes students far less time to learn general relativity now than soon after it was developed because it is understood so thoroughly now that the pedagogy significantly aids the teaching. “Introduction to Quantum Effects in Gravity” is a good example of a pedagogical introduction to a pretty opaque subject.