Lectures on Non-Perturbative Canonical Gravity

Lectures on Non-Perturbative Canonical Gravity

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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 WhyOverviewClassical Theory:Lagrangian FrameworkLegendre Transform: DetailsFrom Triads to SU(2) Spinors: A Quick TransitionHamiltonian FormulationConstraint Algebra, Hamiltonians and DynamicsReality ConditionsInclusion of MatterQuantum Theory:The Quantization ProgramConnection Representation: Linearized GravityConnection Representation: Issue of TimeConnection Representation: CP ProblemLoop Representation: Maxwell TheoryLoop Representation: Classical TheoryLoop Representation: Quantum Theory2+1 GravityAppendices:SpinorsSymplectic FrameworkQuantum Mechanics on ManifoldsQuantization of Constrained SystemsBibliography Readership: Cosmologists, high energy physicists and mathematical physicists. Keywords:General Relativity;Loop Quantum Gravity;Quantum Geometry;Constrained Physical Systems;Algebraic Quantization;Background Independent Methods;Gauge TheoriesReviews:a€œa€b 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 writtena€b. 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.a€Science, 1992 a€œAshtekhar's book may continue to serve as a good pedagogical introduction to the subject.a€General Relativity and Gravitation, 199713.1 Introduction 13.2 CP problem in Yang-Mills theory 13.3 CP problem in quantum gravity 13.4 Discussion LOOP ... CONSTRAINED SYSTEMS BIBLIOGRAPHY 205 207 210 213 217 217 218 223 227 227 229 232 238 241 247 247 248 256anbsp;...

Title:Lectures on Non-Perturbative Canonical Gravity
Author: Abhay Ashtekar
Publisher:World Scientific - 1991-07-03

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