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Modern Canonical Quantum General Relativity

ISBN-10: 0521842638

ISBN-13: 9780521842631

Edition: 2007

Authors: Thomas Thiemann

List price: $214.99
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Description:

Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.
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Book details

List price: $214.99
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 9/13/2007
Binding: Hardcover
Pages: 846
Size: 6.75" wide x 9.75" long x 1.50" tall
Weight: 3.520
Language: English

Notation and conventions
Introduction
Classical Foundations, Interpretation and the Canonical Quantisation Programme
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
Introduction
he holonomy-flux algebra [P]
quantum -algebra
representation theory of [A]
Implementation and solution of the kinematical constraints
implementation and solution of the Hamiltonian constraint
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
Semianalytical 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
Elementary introduction to Gel'fand theory for Abelean C* algebras
Bohr compactification of the real line
Operatir -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 analytical description of classical connection dynamics
Bibliography
Index