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Modern Canonical Quantum General Relativity
monograph
Author(s):
Thomas Thiemann
Publication date
(Online):
2009
Publisher:
Cambridge University Press
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There is no author summary for this book yet. Authors can add summaries to their books on ScienceOpen to make them more accessible to a non-specialist audience.
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Author and book information
Book
ISBN:
9780511755682
Publication date (Print):
2007
Publication date (Online):
2009
DOI:
10.1017/CBO9780511755682
SO-VID:
7453426c-a4f7-4a8e-a10f-f0207aecc367
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Book chapters
pp. xix
Preface
pp. xvii
Foreword, by Chris Isham
pp. xxiii
Notation and conventions
pp. 1
Introduction: Defining quantum gravity
pp. 39
Classical Hamiltonian formulation of General Relativity
pp. 74
The problem of time, locality and the interpretation of quantum mechanics
pp. 107
The programme of canonical quantisation
pp. 118
The new canonical variables of Ashtekar for General Relativity
pp. 141
Introduction
pp. 157
Step I: the holonomy–flux algebra P
pp. 206
Step II: quantum *-algebra A
pp. 212
Step III: representation theory of A
pp. 264
Step IV: (1) implementation and solution of the kinematical constraints
pp. 279
Step IV: (2) implementation and solution of the Hamiltonian constraint
pp. 345
Step V: semiclassical analysis
pp. 399
Extension to standard matter
pp. 431
Kinematical geometrical operators
pp. 458
Spin foam models
pp. 511
Quantum black hole physics
pp. 562
Applications to particle physics and quantum cosmology
pp. 572
Loop Quantum Gravity phenomenology
pp. 575
MATHEMATICAL TOOLS AND THEIR CONNECTION TO PHYSICS
pp. 577
Tools from general topology
pp. 585
Differential, Riemannian, symplectic and complex geometry
pp. 627
Semianalytic category
pp. 634
Elements of fibre bundle theory
pp. 644
Holonomies on non-trivial fibre bundles
pp. 652
Geometric quantisation
pp. 671
The Dirac algorithm for field theories with constraints
pp. 680
Tools from measure theory
pp. 689
Key results from functional analysis
pp. 701
Elementary introduction to Gel'fand theory for Abelian C*-algebras
pp. 713
Bohr compactification of the real line
pp. 719
Operator *-algebras and spectral theorem
pp. 729
Refined algebraic quantisation (RAQ) and direct integral decomposition (DID)
pp. 746
Basics of harmonic analysis on compact Lie groups
pp. 755
Spin-network functions for SU(2)
pp. 770
+ Functional analytic description of classical connection dynamics
pp. 775
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