Modern canonical quantum general relativity
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,...
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| Format: | eBook |
| Language: | English |
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Cambridge
Cambridge University Press
2007
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| Series: | Cambridge monographs on mathematical physics
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| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- 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