Advanced Series in Astrophysics & Cosmology - Vol. 6
LECTURES ON NON-PERTURBATIVE CANONICAL GRAVITY
by Abhay Ashtekar (Syracuse University)
(Notes prepared in Collaboration with Ranjeet S Tate)
It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up-to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.
Contents:
- Introduction:
- Non-Perturbative Quantum
Gravity: What and Why
- Overview
- Classical Theory:
- Lagrangian Framework
- Legendre Transform: Details
- From Triads to SU(2) Spinors: A Quick Transition
- Hamiltonian Formulation
- Constraint Algebra, Hamiltonians and Dynamics
- Reality Conditions
- Inclusion of Matter
- Quantum Theory:
- The Quantization Program
- Connection Representation: Linearized Gravity
- Connection Representation: Issue of Time
- Connection Representation: CP Problem
- Loop Representation: Maxwell Theory
- Loop Representation: Classical Theory
- Loop Representation: Quantum Theory
- 2+1 Gravity
- Appendices:
- Spinors
- Symplectic Framework
- Quantum Mechanics on Manifolds
- Quantization of Constrained Systems
- Bibliography
Readership: Cosmologists, high energy physicists and mathematical
physicists.
"... provides an excellent, up-to-date account of his reformulation of general relativity and of the new approaches to canonical quantum gravity that it has suggested. The book is well organized and well written.... is very successful in achieving its goal of giving a clear, up-to-date introduction to the approach to canonical quantum gravity pioneered by Ashtekar. It is essential reading not only for anyone who intends to do research on this approach but also for anyone at the level of an advanced graduate student or beyond who is interested in broadening his or her perspectives on the theory of quantum gravity."
"Ashtekhar's book may continue to serve as a good pedagogical introduction to the subject."
| General Relativity and Gravitation, 1997 |
| 356pp |
Pub. date: Jul 1991 |
|
