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Canonical quantum gravity : fundamentals and recent developments /
This book aims to present a pedagogical and self-consistent treatment of the canonical approach to Quantum Gravity, starting from its original formulation to the most recent developments in the field. We start with an innovative and enlightening introduction to the formalism and concepts on which Ge...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hackensack, NJ :
World Scientific,
©2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Introduction to general relativity. 1.1. Parametric manifold representation. 1.2. Tensor formalism. 1.3. Affine properties of the manifold. 1.4. Metric properties of the manifold. 1.5. Geodesic equation and parallel transport. 1.6. Levi-Civita tensor. 1.7. Volume element and covariant divergence. 1.8. Gauss and Stokes theorems. 1.9. The Riemann tensor. 1.10. Geodesic deviation. 1.11. Einstein's equations. 1.12. Vierbein representation
- 2. Elements of cosmology. 2.1. The Robertson-Walker geometry. 2.2. Kinematics of the Universe. 2.3. Isotropic Universe dynamics. 2.4. Universe thermal history. 2.5. Inflationary paradigm
- 3. Constrained Hamiltonian systems. 3.1. Preliminaries. 3.2. Constrained systems. 3.3. Canonical transformations. 3.4. Electromagnetic field
- 4. Lagrangian formulations. 4.1. Metric representation. 4.2. ADM formalism. 4.3. Boundary terms
- 5. Quantization methods. 5.1. Classical and quantum dynamics. 5.2. Weyl quantization. 5.3. GNS construction. 5.4. Polymer representation. 5.5. Quantization of Hamiltonian constraints
- 6. Quantum geometrodynamics. 6.1. The Hamiltonian structure of gravity. 6.2. ADM reduction of the Hamiltonian dynamics. 6.3. Quantization of the gravitational field. 6.4. Shortcomings of the Wheeler-DeWitt approach
- 7. Gravity as a gauge theory. 7.1. Gauge theories. 7.2. Gravity as a gauge theory of the Lorentz group? 7.3. Poincare gauge theory. 7.4. Holst action
- 8. Loop quantum gravity. 8.1. Smeared variables. 8.2. Hilbert space representation of the holonomy-flux algebra. 8.3. Kinematical constraints. 8.4. Geometrical operators: discrete spectra. 8.5. The scalar constraint operator. 8.6. Open issues in loop quantum gravity. 8.7. Master constraint and algebraic quantum gravity. 8.8. The picture of quantum spacetime
- 9. Quantum cosmology. 9.1. The minisuperspace model. 9.2. General behavior of Bianchi models. 9.3. Bianchi I model. 9.4. Bianchi IX model. 9.5. BKL conjecture. 9.6. Cosmology in LQG.