View Single Post
marcus is offline
Sep26-10, 05:21 PM
Sci Advisor
PF Gold
marcus's Avatar
P: 22,800
WOW! It is a text book. The field has badly needed a text book focusing on Hamiltonian GR.

It has some 70 exercises for the student to work. And some 40 diagrams/figures/illustrations.

Here is the Table of Contents:

1. Introduction;
2. Isotropic cosmology: a prelude;
3. Hamiltonian formulation of general relativity;
4. Model systems and perturbations;
5. Global and asymptotic properties;
6. Quantum gravity;

There was a real need for this kind of thing. Because for years people have known the ADM version of General Relativity---doing it on a 3D hypersurface with lapse and shift and extrinsic curvature---so that it is equivalent to the 4D treatment. For decades we have had a Hamiltonian formulation of GR. And in fact most of the NUMERICAL work, so I am told, uses this by preference. And this version gave rise to the Ashtekar new variables, a gauge theoretical formulation, and LQG.

And yet the canonical GR, the Hamiltonian version, tends to be neglected in undergraduate courses.

The form of GR that you will use if you want to do numerical work on computer, or if you want to do LQG, is a form you might only meet later in grad school! So this was wrong and Bojowald seems to be offering to fix the problem.

Here now is a GR textbook that presents the canonical GR, with Hamiltonian. And then even proceeds on to a chapter about Quantum Gravity. Maybe we can learn something from the Cambridge Press description:

==quote from the publisher's description==

Canonical methods are a powerful mathematical tool within the field of gravitational research, both theoretical and experimental, and have contributed to a number of recent developments in physics. Providing mathematical foundations as well as physical applications, this is the first systematic explanation of canonical methods in gravity. The book discusses the mathematical and geometrical notions underlying canonical tools, highlighting their applications in all aspects of gravitational research from advanced mathematical foundations to modern applications in cosmology and black hole physics. The main canonical formulations, including the Arnowitt-Deser-Misner (ADM) formalism and Ashtekar variables, are derived and discussed. Ideal for both graduate students and researchers, this book provides a link between standard introductions to general relativity and advanced expositions of black hole physics, theoretical cosmology or quantum gravity.

• Gives a thorough account of gravity theory, from advanced mathematical foundations to modern applications in cosmology and black hole physics • Provides mathematical foundations as well as physical applications to give a systematic explanation of canonical methods in gravity • Touches on large areas of theoretical gravitational research: cosmology, black holes, quantum gravity