Research Catalog

Details

Description

1. xxvi, 819 pages : illustrations; 26 cm.

Summary

1. "This book provides a complete treatise of the canonical quantization of general relativity. The focus is on detailing the conceptual and mathematical-framework, describing the physical applications; and summarizing the status of this program in its most popular incarnation: Joop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, so it is suitable for graduate-students and researchers with a basic knowledge of quantum field theory and general relativity."--Jacket.

Series statement

1. Cambridge monographs on mathematical physics

Uniform title

1. Cambridge monographs on mathematical physics.

Subject

1. Quantum theory
2. General relativity (Physics)
3. Théorie quantique
4. Relativité générale (Physique)
5. Quantum theory

Contents

1. Defining quantum gravity -- Classical Hamiltonian formulation of general relativity -- The problem of time, locality, and the interpretation of quantum mechanics -- The programme of canonical quantisation -- The new canonical variables of Ashtekar for general relativity -- Foundations of modern canonical quantum general relativity --Step I : the holonomy-flux algebra -- Step II : quantum algebra -- Step III : representation theory -- Step IV : (1) implementation and solution of the kinematical constraints -- Step IV (2) : impelementation and solution of the Hamiltonian constraint -- Step V : semiclassical analysis -- Physical applications -- Extension to standard matter -- Kinematical geometrical operators -- Spin foam models -- Quantum black hole physics -- Applications to particle physics and quantum cosmology -- Loop quantum gravity phenomenology -- Mathematical tools and their connection to physics -- Tools from general topology -- Differential, Riemannian, symplectic, and complex geometry -- Semianalytic category -- Elements of fibre bundle theory -- Holonomies on non-trivial fibre bundles -- Geometric quantisation -- The Dirac algorithm for field theories with constraints -- Tools from measure theory -- Key results from functional analysis -- Elementary introduction to Gel'fand theory for Abelian C*-algebras -- Bohr compactification of the real line -- Operator *-algebras and spectral theorem -- Refined algebraic quantisation (RAQ) and direct integral decomposition (DID) -- Basics of harmonic analysis on compact Lie groups -- Spin-network functions for SU (2) -- + Functional analytic description of classical connection dynamics.

Owning institution

1. Harvard Library

Bibliography (note)

1. Includes bibliographical references and index.

Processing action (note)

1. committed to retain