Modern canonical quantum general relativity

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Modern canonical quantum general relativity / Thomas Thiemann

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2008
形態:: xxvi, 819 p. ; 25 cm
シリーズ名:: Cambridge monographs on mathematical physics <BA00074521>
著者名:: Thiemann, Thomas
ISBN:: 9780521741873 [0521741874] (: pbk)
書誌ID:: BB00224202

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注記:

Includes bibliographical references and index

主題:

General relativity (Physics); Quantum theory

言語:

英語

目次情報:

Preface

Notation and conventions

Introduction

Classical Foundations, Interpretation and the Canonical Quantisation Programme / Part I：

Classical Hamiltonian formulation of general relativity / 1：

The problem of time, locality and the interpretation of quantum mechanics / 2：

The programme of canonical quantisation / 3：

The new canonical variables of Ashtekar for general relativity / 4：

Foundations of Modern Canonical Quantum General Relativity / Part II：

Step I: the holonomy-flux algebra [P] / 5：

Step II: quantum-algebra / 7：

Step III: representation theory of [A] / 8：

Step IV / 9：

Implementation and solution of the kinematical constraints

Step V / 10：

Implementation and solution of the Hamiltonian constraint

Step VI: semiclassical analysis / 11：

Physical Applications / Part III：

Extension to standard matter / 12：

Kinematical geometrical operators / 13：

Spin foam models / 14：

Quantum black hole physics / 15：

Applications to particle physics and quantum cosmology / 16：

Loop quantum gravity phenomenology / 17：

Mathematical Tools and their Connection to Physics / Part IV：

Tools from general topology / 18：

Differential, Riemannian, symplectic and complex geometry / 19：

Semianalytical category / 20：

Elements of fibre bundle theory / 21：

Holonomies on non-trivial fibre bundles / 22：

Geometric quantisation / 23：

The Dirac algorithm for field theories with constraints / 24：

Tools from measure theory / 25：

Elementary introduction to Gel'fand theory for Abelean C* algebras / 26：

Bohr compactification of the real line / 27：

Operatir -algebras and spectral theorem / 28：

Refined algebraic quantisation (RAQ) and direct integral decomposition (DID) / 29：

Basics of harmonic analysis on compact Lie groups / 30：

Spin network functions for SU(2) / 31：

+ Functional analytical description of classical connection dynamics / 32：

Bibliography

Index

Preface

Notation and conventions

Introduction

Classical Foundations, Interpretation and the Canonical Quantisation Programme / Part I：

Classical Hamiltonian formulation of general relativity / 1：

The problem of time, locality and the interpretation of quantum mechanics / 2：

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