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Quantum Gravity (Cambridge Monographs on Mathematical Physics) 1st Edition

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ISBN-13: 978-0521715966
ISBN-10: 0521715962
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Editorial Reviews


"This is a truly great book!...a must for someone interested in quantum gravity." -
Mathematical Reviews, Jose A. Zapata

"... an excellent text for graduate courses."
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Book Description

Quantum gravity is one of the major open problems in theoretical physics. The loop and spinfoam approach, presented in this book, is a leading research program in the field. Emphasis is given to conceptual and foundational issues raised by quantum gravity, especially on the nature of space and time. This text is intended for researchers working in quantum gravity and, in particular, graduate students entering the field. It will also appeal to philosophers and scientists interested in the general issue of the nature of space and time.

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Product Details

  • Series: Cambridge Monographs on Mathematical Physics
  • Paperback: 488 pages
  • Publisher: Cambridge University Press; 1 edition (December 17, 2007)
  • Language: English
  • ISBN-10: 0521715962
  • ISBN-13: 978-0521715966
  • Product Dimensions: 6.8 x 1 x 9.7 inches
  • Shipping Weight: 2.1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #1,630,246 in Books (See Top 100 in Books)

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31 of 35 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on April 24, 2005
Format: Hardcover Verified Purchase
This book gives a detailed overview of that "other theory" of quantum gravity called `loop quantum gravity'. String theory has been viewed by many as a promising theory of quantum gravity and there are many reasons to believe this is the case. String theory though requires a formidable amount of mathematics for its construction, and has yet to have any experimental verification. Therefore, it is not surprising that other alternative theories of quantum gravity would be constructed, these needing a minimal amount of formalism and staying as close as possible to what can be observed. Loop quantum gravity is one of these, and is the most popular alternative to string theory as a theory of quantum gravity.

The initial five chapters of the book motivate the need for quantum gravity and also phrase the theories of general relativity and relativistic quantum physics in a language that will be used to formulate the theory of loop quantum gravity. General relativity (GR) is formulated as a dynamical system defined by the Hamilton-Jacobi equation for a functional defined on the space G of three-dimensional SU(2) connections. The equation is invariant under internal gauge transformations and 3D diffeomorphisms.

The quantization of GR is obtained in terms of complex-valued Schrodinger wave functionals on G. The derivatives of the Hamilton-Jacobi functional are replaced by derivative operators in order to obtain the quantum dynamics. The Hamilton-Jacobi equation then becomes the Wheeler-DeWitt equation governing the quantum dynamics of spacetime. The quantum (kinematical) state space is defined letting G be the space of smooth 3D real connections defined everywhere on a 3D surface S.
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15 of 18 people found the following review helpful By Douglas Mckenzie on December 8, 2005
Format: Hardcover Verified Purchase
I'm experiencing some hesitation as this is hands down the most advanced book that I have ever 'reviewed' and, in fact, ever read. I have only completed Part 1 -"Relativistic Foundations" as I have to go deeper into Differential Geometry before proceeding into Part II - "Loop Quantum Gravity." Part 1 is a pretty amazing, often philosophical introduction both describing the problem that QG is trying to approach (the contradictions between QFT and GR)and laying the foundation for LQG. It becomes clear (slowly) that our notions of space and time need serious overhauling before we can understand what LQG is all about. String theory doesn't have this problem as it more or less uses our 20th century notions of space and time as its framework. Sure, it adds a few dimensions and curls some up but it's pretty much still the same old space and time. LQG does not use this framework and rather seems to work towards a physics without time. Rovelli does a masterful job in Part 1 of slowly, clearly and precisely helping the reader to make this transition. Most memorable to me is his discusson of the ten meanings of time where he demonstrates that we have already stripped time of many of its seemingly inherent properties ('flowing', 'measured' to name 2). He just proposes stripping off a few others! I'm looking forward to Part II.
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20 of 25 people found the following review helpful By Dean Welch on March 15, 2006
Format: Hardcover
I have to start by saying that I think the title is very deceptive. This is hardly a book on quantum gravity, more accurately it's a book on one approach to quantum gravity, namely loop quantum gravity. No other approaches to quantum gravity are seriously considered. Even the current leading candidate for providing a quantum theory of gravity, i.e. string theory, is only presented as a straw man to show how poorly it fares (in the author's mind) compared to loop quantum gravity.

The book begins with a brief discussion on general issues in quantum gravity and by presenting some background in general relativity.

He contends that it is wrong to approach quantum gravity by treating general relativity as just another field theory. Two central themes of his approach to quantum gravity seem to be that one should not ignore the fact that general relativity is a theory of spacetime and the correct way to approach finding the quantum theory of gravity (although I don't believe he uses these exact words) is to quantize spacetime. This will lead to spacetime having a discrete structure and will provide a cutoff that will remove the ultraviolet divergences of quantum field theory (this is somewhat different from the way they are removed in string theory). While I agree both of these ideas have a lot of intuitive appeal, it's clear that the jury is still out.

The treatment of general relativity focuses mainly on things that will be useful for developing loop quantum gravity. This includes formulating it in terms of connections (instead of the metric) and presenting it in the Hamiltonian form.
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8 of 9 people found the following review helpful By G. T. Bennett on August 2, 2006
Format: Hardcover
This is a excellent book. Dr. Rovelli is attempting a rare exercise in that he is trying to substantially change a physicists view of the world. This book is equal parts philosphy and mathematics and tries to instill in the reader an intuition that most books never achieve. The book is not for someone who likes to be given an equation or model and then is shown how to "turn the crank" to obtain an answer or those who think the theory is finished as long as you constrain yourself to stay away from the pathologies. (Think Standard Model and a single photon that has the energy density of a black hole. ) Most present day theories have these pathologies, patches and inconsistencies precisely because they were built from previous approximate theories and then were modified when problems showed up. This book starts with a clean sheet of paper and asks, "What should a relativistic quantum theory of gravity look like?' "What are the mathematical structures that are needed and how do they fit together to give us a consistent view of the world?" Indeed the book goes back through classical mechanics and quantum just to show what the mathematical structures do in each of these early theories. The philosophical basis, the "why is this important", for the combination of quantum ideas and the philosophy of relativism is very well laid out in this book. That is what I was seeking, "the why". Theories that throw another constraint on the space of solutions, or add more symmetry just to fix problems that pop up means that they have serious flaws in their basic foundations that need to be addressed differently. Dr. Rovelli shows that loop quantum gravity has the same clean sparseness as it's foundations and is very appealing. The discrete quantization of volume and area is a major sucess. If you like having your world view changed, a new paradigm, I highly recommend this book.
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