Book contents
- Frontmatter
- Contents
- Foreword, by Chris Isham
- Preface
- Notation and conventions
- Introduction: Defining quantum gravity
- I CLASSICAL FOUNDATIONS, INTERPRETATION AND THE CANONICAL QUANTISATION PROGRAMME
- II FOUNDATIONS OF MODERN CANONICAL QUANTUM GENERAL RELATIVITY
- III PHYSICAL APPLICATIONS
- IV MATHEMATICAL TOOLS AND THEIR CONNECTION TO PHYSICS
- 18 Tools from general topology
- 19 Differential, Riemannian, symplectic and complex geometry
- 20 Semianalytic category
- 21 Elements of fibre bundle theory
- 22 Holonomies on non-trivial fibre bundles
- 23 Geometric quantisation
- 24 The Dirac algorithm for field theories with constraints
- 25 Tools from measure theory
- 26 Key results from functional analysis
- 27 Elementary introduction to Gel'fand theory for Abelian C*-algebras
- 28 Bohr compactification of the real line
- 29 Operator *-algebras and spectral theorem
- 30 Refined algebraic quantisation (RAQ) and direct integral decomposition (DID)
- 31 Basics of harmonic analysis on compact Lie groups
- 32 Spin-network functions for SU(2)
- 33 + Functional analytic description of classical connection dynamics
- References
- Index
19 - Differential, Riemannian, symplectic and complex geometry
Published online by Cambridge University Press: 04 August 2010
Book contents
- Frontmatter
- Contents
- Foreword, by Chris Isham
- Preface
- Notation and conventions
- Introduction: Defining quantum gravity
- I CLASSICAL FOUNDATIONS, INTERPRETATION AND THE CANONICAL QUANTISATION PROGRAMME
- II FOUNDATIONS OF MODERN CANONICAL QUANTUM GENERAL RELATIVITY
- III PHYSICAL APPLICATIONS
- IV MATHEMATICAL TOOLS AND THEIR CONNECTION TO PHYSICS
- 18 Tools from general topology
- 19 Differential, Riemannian, symplectic and complex geometry
- 20 Semianalytic category
- 21 Elements of fibre bundle theory
- 22 Holonomies on non-trivial fibre bundles
- 23 Geometric quantisation
- 24 The Dirac algorithm for field theories with constraints
- 25 Tools from measure theory
- 26 Key results from functional analysis
- 27 Elementary introduction to Gel'fand theory for Abelian C*-algebras
- 28 Bohr compactification of the real line
- 29 Operator *-algebras and spectral theorem
- 30 Refined algebraic quantisation (RAQ) and direct integral decomposition (DID)
- 31 Basics of harmonic analysis on compact Lie groups
- 32 Spin-network functions for SU(2)
- 33 + Functional analytic description of classical connection dynamics
- References
- Index
- Type
- Chapter
- Information
- Modern Canonical Quantum General Relativity , pp. 585 - 626Publisher: Cambridge University PressPrint publication year: 2007