A First Course in Loop Quantum Gravity (英語) ハードカバー – 2011/11
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This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.
I highly recommend this book ... Congratulations to the authors for the great, concise, effective presentation of this challenging field to students and interested researchers coming from other fields. (Christine Córdula Dantas, Toy Universes)
Gambini and Pullin have written an excellent and truly introductory book, aimed at the undergraduate level, which fills a gap in the existing literature, and responds to the growing interest in this subject. (Carlo Rovelli, Aix-Marseille University, France)
Loop quantum gravity is currently one of the main approaches in the search for a quantum theory of gravity. Written by well-known experts in this field, "A First Course in Loop Quantum gravity" is the first book on this topic that is accessible already to undergraduates. No previous knowledge of general relativity and quantum field theory is required; instead, the necessary material from these subjects is introduced in a clear and pedagogical way. The authors present the key features of loop quantum gravity, but also do not hide its weak points. The book can be recommended to anyone from student to established scientist who wants to get a short, reliable, and clear introduction to this fascinating field of research. (Claus Kiefer, University of Cologne, Germany)
Marvellously succeeds in starting from the basics of special relativity and covering basic topics in Hamiltonian dynamics, Yang Mills theory, general relativity and quantum field theory, ending with a tour on current (loop) quantum gravity research. This is done in a short 192 pages! (Bianca Dittrich, IOP Publishing)
One approach to a quantum theory of gravity is the famous (perhaps infamous) "string theory". Another approach, the approach discussed in this book, is loop quantum gravity, in which a more traditional approach to quantizing the gravitational field is employed. In a nutshell, loop quantum gravity is a canonical quantization of a modification of the Hamiltonian formulation of general relativity originally developed by Arnowitt, Deser, and Misner in the early 1960s ("ADM formalism"), said modification being the replacement of the position and momentum variables used by ADM with a new set of variables introduced by Ashtekar in the 1980s. Canonical quantization refers to the quantization procedure based on the Hamiltonian originally developed by Dirac in the 1920s and further developed by him in the 1950s. Loop quantum gravity uses a "loop representation" which has as a key result that there is a minimum allowed length, area, and volume in the universe, i.e, these quantities are quantized. This in turn leads to the result that the universe has a minimum size, and if we play the movie of cosmic expansion backwards, we reach this minimum size before we reach the singularity, and the universe starts to expand again, the so-called "Big Bounce". Also, the relation between the surface area and entropy of a black hole reduces to a relationship between the number of area quanta which make up the surface area and the entropy.
This book is directed at the advanced undergraduate level, and aims to fill a gap in the pedagogy of this subject, which requires much more math and physics background to really understand than any undergraduate would have. As a result, it takes a very simplistic approach and should be considered no more than a very preliminary introduction to the topic.
The first part of the book covers all the basic background concepts needed to understand the program of loop quantum gravity, including general relativity, the generalized Hamiltonian with constraints, and canonical quantization. It then goes on to discuss the ADM formalism, Ashtekar variables, the loop representation, and applications of loop quantum gravity to cosmology and black hole thermodynamics. It ends with a very honest evaluation of the limitations and incompleteness of the theory at the present time. Loop quantum gravity is still a work in progress, and although there have been many important advances in terms of formulating a theory, there is as yet no validation experimentally, nor any obvious path to such a validation.
You will not really understand loop quantum gravity when you finish this book, only understand a very superficial version of it "dumbed down" for the intended readership of this book, but still extremely formidable in terms of its demands on the reader mathematically speaking. If you haven't already had at least an introductory exposure to general relativity, quantum mechanics, Lagrangian and Hamiltonian mechanics, and quantum field theory, you're in for some very tough sledding indeed. If you have this background, after you finish this book you will be prepared to delve more deeply into the topic if you have the time and inclination. Included are references to more advanced texts as well as important review papers to guide this further exploration.
I give this book 5 stars for identifying a pedagogical need, clearly defining the intended readership and the goals, and carefully describing the inevitable limitations and gaps in trying to present such a sophisticated, difficult topic to a relatively unprepared audience.
I give it three stars for the attempt, but I don't actually think it's possible to teach LQG at an undergraduate level.
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