A First Course in Loop Quantum Gravity
Posted Nov26-11 at 05:50 PM by aalaniz
Depending on your background, the introductorry book on Loop Quantum Gravity by Gambini and Pullin is a pretty good and succint. As a non-specialist who likes keeping current with today's foundation physics, I found my readings from the following sources to be pretty essential:
For Gambini's and Pullin's chapters 2 and 3:
1) "A Short Course in General Relativity" by J. Foster and J. D. Nightingale.
For Gambini's and Pullin's chapters 4-6:
2)"Quantum Field Theory," 2nd ed., by L. H. Ryder (or an equivalent text). I like Ryder, but Peshkin and Schroeder is one alternative among many.
3) "Classical Mechanics," 2nd ed., by H. Goldstein, chapters 8 and 9 on the Hamilton equations of motion and Canonical transforamtions. When I read Goldstein, I also read, "Variational Principles in Dynamics and Quantum Mechanics," W Yourgrau and S. Mandelstam--a great history of the evolution of mechanics!
4) I have a pretty good feel of Lie groups/Lie Algebras from "Lie Groups, Lie Algebras, and Some of Their Applications" by R. Gilmore chapters 1-4.
Gilmore does a really good job of developing the theory in his book with an example he stretches out chapter by chapter so that the reader has at least one toy example to match a bunch of theory wrapped in a bunch of notation, especially in his (Gilmore's) chapter 3 and 4. This would be a great thing to include in Gambini's and Pullin's text in section 3.5, and especially in sections 3.6 and 3.7, essential sections to understand if you're brand new to LQG.
It would probably not be a bad idea to understand the use of forms, say at the level of "Geometry, Topology and Physics" by M. Nakahara for "pullbacks", the Lie derivative (chapter 5), and chapters 9 and 10 on connectins and curvature in a modern, "forms" setting.
Gambini's and Pullin's material in 3.5 through 3.7 come back hard starting from 7.2 in the presentation of Ashtekar's variables.
Without reviewing the above material, and very likely some of the review material suggested by Gambini and Pullin, I don't think I can any better than some fuzzy idea of LQG from this text.
Cheers,
Alex
For Gambini's and Pullin's chapters 2 and 3:
1) "A Short Course in General Relativity" by J. Foster and J. D. Nightingale.
For Gambini's and Pullin's chapters 4-6:
2)"Quantum Field Theory," 2nd ed., by L. H. Ryder (or an equivalent text). I like Ryder, but Peshkin and Schroeder is one alternative among many.
3) "Classical Mechanics," 2nd ed., by H. Goldstein, chapters 8 and 9 on the Hamilton equations of motion and Canonical transforamtions. When I read Goldstein, I also read, "Variational Principles in Dynamics and Quantum Mechanics," W Yourgrau and S. Mandelstam--a great history of the evolution of mechanics!
4) I have a pretty good feel of Lie groups/Lie Algebras from "Lie Groups, Lie Algebras, and Some of Their Applications" by R. Gilmore chapters 1-4.
Gilmore does a really good job of developing the theory in his book with an example he stretches out chapter by chapter so that the reader has at least one toy example to match a bunch of theory wrapped in a bunch of notation, especially in his (Gilmore's) chapter 3 and 4. This would be a great thing to include in Gambini's and Pullin's text in section 3.5, and especially in sections 3.6 and 3.7, essential sections to understand if you're brand new to LQG.
It would probably not be a bad idea to understand the use of forms, say at the level of "Geometry, Topology and Physics" by M. Nakahara for "pullbacks", the Lie derivative (chapter 5), and chapters 9 and 10 on connectins and curvature in a modern, "forms" setting.
Gambini's and Pullin's material in 3.5 through 3.7 come back hard starting from 7.2 in the presentation of Ashtekar's variables.
Without reviewing the above material, and very likely some of the review material suggested by Gambini and Pullin, I don't think I can any better than some fuzzy idea of LQG from this text.
Cheers,
Alex
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