| Description |
1 online resource |
| Contents |
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 |
| Summary |
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 General Relativity has been built, giving all the information necessary in the later analysis. A brief sketch of the Standard Cosmological Model describing the Universe evolution is also given alongside the analysis of the inflationary mechanism. After deepening the fundamental properties of constrained dynamic systems, the Lagrangian approach to the Einsteinian Theory is presented in some detail, underlining the parallelism with non-Abelian gauge theories. Then, the basic concepts of the canonical approach to Quantum Mechanics are provided, focusing on all those formulations which are relevant for the Canonical Quantum Gravity problem. The Hamiltonian formulation of General Relativity and its constrained structure is then analyzed by comparing different formulations. The resulting quantum dynamics, described by the Wheeler CDeWitt equation, is fully discussed in order to outline its merits and limits. Afterwards, the reformulation of Canonical Quantum Gravity in terms of the Ashtekar CBarbero CImmirzi variables is faced by a detailed discussion of the resulting Loop Quantum Gravity Theory. Finally, we provide a consistent picture of canonical Quantum Cosmology by facing the main features of the Wheeler CDeWitt equation for the homogeneous Bianchi models and then by a detailed treatment of Loop Quantum Cosmology, including very recent developments |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Quantum gravity.
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Gravitation.
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General relativity (Physics)
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Gravitation
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SCIENCE -- Energy.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Physics -- General.
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General relativity (Physics)
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Gravitation
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Quantum gravity
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| Form |
Electronic book
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| Author |
Lecian, Orchidea Maria, 1980-
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Lulli, Matteo.
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Montani, Giovanni, 1966-
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| ISBN |
9789814556651 |
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9814556653 |
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1306941997 |
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9781306941990 |
|
