Download PDF A First Course in Loop Quantum Gravity, by Rodolfo Gambini, Jorge Pullin
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A First Course in Loop Quantum Gravity, by Rodolfo Gambini, Jorge Pullin
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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.
To request a copy of the Solutions Manual, visit: http://global.oup.com/uk/academic/physics/admin/solutions
- Sales Rank: #1087122 in Books
- Published on: 2011-11-01
- Original language: English
- Number of items: 1
- Dimensions: 6.90" h x .60" w x 9.80" l, 1.06 pounds
- Binding: Hardcover
- 192 pages
Review
"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
From Oxford University Press' website.
... the first book on this topic that is accessible already to undergraduates. No previous knowledge of general relativity and quantum field theory is required... The authors present the key features of loop quantum gravity, but also do not hide its weak points. - Claus Kiefer, University of Cologne, Germany From Oxford University Press' website
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 Cordula 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
About the Author
Rodolfo Gambini did his undergraduate work at the University of the Republic of Uruguay, went for a Ph.D. at the University of Paris and joined the faculty at the Universidad Simon Bolivar in Venezuela. He returned to Uruguay in 1997 where he has been director of several government funding agencies in addition to being a Professor at the University of the Republic. He has won the Trieste Prize in Physics, the presidential prize for scientific accomplishment in Uruguay and received an honorary doctorate from the University of the Republic.
Jorge Pullin did his undergraduate work at the Instituto Balseiro in Bariloche, Argentina, did his Ph.D. thesis work at the University of Cordoba and moved as a post-doc to Syracuse University and the University of Utah. He became a faculty member at PennState and in 2001 joined the Louisiana State University as the Horace
Hearne Chair in Theoretical Physics. He is the co-director of the Horace Hearne Institute of Theoretical Physics and the interim co-director of the Center for Computation and Technology at the Louisiana State University. He was the chair of the Topical Group in Gravitation of the American Physical Society and served on the editorial boards of Classical and Quantum Gravity and the New Journal of Physics and is currently on the board of Living Reviews, Papers in Physics and is managing editor of International Journal of Modern Physics D.
Most helpful customer reviews
26 of 28 people found the following review helpful.
Finally, a real introduction to the field.
By Christine C. Dantas
If you are looking for an introduction to Loop Quantum Gravity that *really* guides you through every *minimum* required piece of knowledge at the basis of this field, including an outline of the mathematics involved, in order to put you in a comfortable position to enter the research literature, then there is (currently) no better place to start.
It has always been a mystery to me why Rovelli's book, for instance, is generally considered as "introductory". Although it is a very well written book by one of the experts in the field, and obligatory reading for those seriously interested in studying the matter, readers who had never - or only slightly - been exposed to Loop Quantum Gravity will find it quite advanced at various places. The same occurs with other similar books in this field, considered "introductory": they may be so at places, but... only to the extent of your background, which seems an amusing way to put it, if not frustrating: "introductory-but-not-exactly-so".
That does not happen with Gambini and Pullin's book. It is indeed the only current *real* introductory, (not laymen, but mathematically-based!), self-study textbook on Loop Quantum Gravity. All other current books in the field - Rovelli's, Kiefer's, Thiemann's, etc - are excellent references to be studied *after* Gambini and Pullin's book. Finally, the basics of Loop Quantum Gravity is available in textbook form!
"A First Course in Loop Quantum Gravity" is in fact aimed at the advanced undergraduate level, and it does a great job to follow that difficult requirement. However, it is unavoidable that even an average reader at that level will have to accept some concepts without further detailed background. Gratefully, the authors are careful enough to state that explicitly, what is going on and why, and to offer a good, minimal list of references to follow at the end of each chapter, so that the reader can attempt studying the details. Various of these references are freely available in the internet as expository or review papers. There are also problems at the end of each chapter, suitable to self-study, as they are of the type: "prove", "show", "derive", "compute"... I believe that some of these problems will be regarded somewhat difficult for an undergraduate student. They are however excellent complements to the main text and should be seriously attempted.
The book is very pleasant to read and very clear. It is also amazingly concise and objective. I really like the way the authors expose every subtlety behind the theory; the "tips" and analogies offered throughout the text are really excellent, and effectively helped me to finally understand a few concepts which were confusing to me until recently.
The reader should, however, be advised that the contents are intrinsically advanced. It is definitely not for the common reader, it is a technical book. It is not an easy field anyway, as Loop Quantum Gravity obviously requires deep knowledge of quantum mechanics and general relativity, as well as several advanced mathematical concepts. But be sure that the authors will teach you what are the minimal required elements of these pre-requisites, so you will at least be aware of them and be able to pursue them further by yourself.
I highly recommend this book for anyone with complete undergraduate courses in physics and mathematics. With my own main background in astrophysics, I can say this book is also a great introduction for astronomers/astrophysicists/cosmologists who never studied Loop Quantum Gravity. A good complement in that regard (applications) would be Bojowald's books "Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity" and "Quantum Cosmology: A Fundamental Description of the Universe", apart from the more advanced books already cited above (e.g., the obligatory and excellent books by Rovelli, Kiefer, Thiemann...). Finally, there is of course freely available review material in the arxiv site.
Congratulations to the authors for the great, concise, effective presentation of this challenging field to students and interested researchers coming from other fields.
7 of 8 people found the following review helpful.
the first step on a thousand mile journey
By arpard fazakas
Many non-experts who are interested in physics know that the current theory of gravity, Einstein's general theory of relativity, stands apart from the theories of the other three fundamental forces, the electromagnetic, weak nuclear, and strong nuclear forces, in that the former is a classical theory whereas the latter are quantum theories. Physicists like to unify things, so they would like to have the theory of gravity be a quantum theory as well, so they can then have a "theory of everything". In addition to being satisfying on a philosophical and esthetic level, this would also potentially be able to explain what's going on at the center of black holes and at the "beginning" of the Big Bang, for which general relativity gives a singularity, an unphysical point of infinite energy density indicating that general relativity is no longer properly describing the physical reality in these situations.
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.
3 of 3 people found the following review helpful.
Nice Overview of the physics involved in the quantization of Gravity (put aside string theory)
By Ricardo Avila
This book contains a nice overview of the Physics involved in the more traditional approach to quantizing gravity, that is Loop Quantum Gravity (LQG). It is important to say though that all the topics treated are only superficially presented which I suppose it is ok considering the audience it is target at, that is, advanced undergraduates who have not yet had a real exposure to topics like Classical Field Theory, Quantum Field Theory, Dirac's theory of Constraints and General Relativity. Having said this I must say that the book gives you not so much formulas but the really important (and necessary), the rest is very nicely explained with words, so it reads much as a story. It starts by revising special relativity and the formulation of Maxwell's electrodynamics both first through the usual approach and then using relativistic tensorial formulation. Then it proceeds to present General Relativity first giving the basics of curved geometry, i.e. vectors, tangent spaces and the jumping straight to curvature. After this, Einsteins equations are presented along with two of its exact solutions: the Schwarszchild and Robertson-Walker spacetimes, also a word on diffeomorphisms and the Lie derivative are given. Then the famous 3+1 decomposition of GR is given, this is, the ADM (Arnowitt-Deser-Misner) formulation and the metric is also decomposed in triads which will be essentially used later as one of the canonically variables of the reformulation of GR. After this the theory of Hamiltonian mechanics with constraints is given and then Yang-Mills theories. Then the authors reminds about quantum mechanics, and the generalization of this to field theories, quantum field theories, a brief introduction to interacting field theories is given explaining how divergences appear in perturbative series where also Feynman diagrams are illustrated. Finally a word on renormalization is also given. After this the reformulation of General Relativity in terms of the new Ashtekar's variables is presented. All the grace of this new change of variable is that now GR can be written much similar to a usual Yang Mills theory and originally there was hope that since YM were known on as how to quantize them, the same would happen here but unfortunately the Hamiltonian Constraint is either complex (and simple) or is real and so complicated that it has not been solved until this day. Toward the end of the book are presented loop variables, the concept of spin networks, mentioned the result that in loop quantum gravity there is an Area and Volume operator and so area and volume in this theory are quantize, there is a chapter on loop quantum cosmology and finally the last chapter touches upon some known facts about black holes like Hawking Radiation and black hole entropy, spin foams which are basically the many spin networks intertwined together as you move from one geometry to another in the path integral for GR, some possible experiments that could be done to test this theory and the Loved by me and intriguing "Problem of Time" which basically consists in that as the Hamiltonian of GR is just a sum of constraints and on the other part constraints vanish weakly, the whole thing (i.e. the entire Hamiltonian) vanishes and by hamilton's equations this implies that there is no evolution in time of any dynamical variable, in other words, the whole system is frozen!, well I like the book and give to it four stars because sometimes is just a little too sloppy on some of the material presented although when it is, it does gives you a proper reference to look at for further study, all in all, nice book!
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