Quantum Gravity in 2+1 Dimensions (Cambridge Monographs on Mathematical Physics)

Rating:
Summary: Carlip's 2+1 dimensional Quantum Gravity
Review: This is the outstanding reference and survey book for quantum gravity in 2 spatial and 1 time dimensions, and also has a number of Carlip's own recent contributions. When quantum gravity (QG for short) is restricted to 2 spatial dimensions, it simplifies analysis enormously, both physically and mathematically. I have cited Carlip's book both in papers delivered at conferences and in publications. Here is the opportunity to understand different schools of quantum gravity, including the Hawking-Hartle school and its comparison with the closely related Lortentian metric (v.s. Euclidean metric) school, the Ashtekar-Smolin loop school, the Wheeler-Dewitt equation school, the lattice school, the Feymann path integral school, the black hole entropy schools (to which both Carlip and Hawking/Penrose have contributed), various algebraic and topological schools, the incredibly rich moduli space and modular transformation results, and so on. Unlike most books, Carlip's is open minded regarding different schools, and gives comparisons and criticisms which are invaluable. The non-expert in quantum gravity would be well advised to start learning from this book and a few very clear mathematics and physics books (or to hire a consultant or even a tutor to explain prerequisites and some of the mathematical concepts in the book), because the average quantum gravity book is almost totally incomprehensible for non-experts compared with Carlip. I consider Carlip's clarity and comparisons between different schools to be far superior to even Hawking's, although of course Hawking is almost unrivaled as a physicist. The nearest you will come to Carlip's presentation is by reading hundreds of journal articles and books, which is impractical for most people.

Rating:
Summary: Carlip's 2+1 dimensional Quantum Gravity
Review: This is the outstanding reference and survey book for quantum gravity in 2 spatial and 1 time dimensions, and also has a number of Carlip's own recent contributions. When quantum gravity (QG for short) is restricted to 2 spatial dimensions, it simplifies analysis enormously, both physically and mathematically. I have cited Carlip's book both in papers delivered at conferences and in publications. Here is the opportunity to understand different schools of quantum gravity, including the Hawking-Hartle school and its comparison with the closely related Lortentian metric (v.s. Euclidean metric) school, the Ashtekar-Smolin loop school, the Wheeler-Dewitt equation school, the lattice school, the Feymann path integral school, the black hole entropy schools (to which both Carlip and Hawking/Penrose have contributed), various algebraic and topological schools, the incredibly rich moduli space and modular transformation results, and so on. Unlike most books, Carlip's is open minded regarding different schools, and gives comparisons and criticisms which are invaluable. The non-expert in quantum gravity would be well advised to start learning from this book and a few very clear mathematics and physics books (or to hire a consultant or even a tutor to explain prerequisites and some of the mathematical concepts in the book), because the average quantum gravity book is almost totally incomprehensible for non-experts compared with Carlip. I consider Carlip's clarity and comparisons between different schools to be far superior to even Hawking's, although of course Hawking is almost unrivaled as a physicist. The nearest you will come to Carlip's presentation is by reading hundreds of journal articles and books, which is impractical for most people.

Rating:
Summary: A thorough exposition
Review: Written by arguably the leading expert in the field, this monograph is a concise exposition on the many *exact* quantizations of Einstein's equation in 2+1 dimensions. As pointed out in the introduction, the text deals almost entirely with quantization of the vacuum equations, albeit with and without a cosmological constant. [Readers looking for results on the subject of cosmic string research, along the lines of 't Hooft's work, should look elsewhere.] Several complimentary formal approaches to quantization are covered and contrasted; e.g., Hamiltonian frameworks ala the Wheeler Dewitt equation, the Palintini / Ashtekhar new variables, Euclidean and Lorentzian path integration, and even Regge calculus --- to name a few. Included chapters also cover a field quide to classical solutions --- such as the BTZ black hole -- as well as Carlip's own ground breaking work on counting the quantum states of Hawking radiation. Finally, an appendix courteously describes several results from topology that are not unusually at a physicists beck and call. Overall, this is a *clearly* written text that uses the `laboratory' of exact quantum gravity in 2+1 dimensions to boldly face the many conceptual difficulties -- such as the problems of time and topology change -- found in any attack on the quantization of space of time.