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Author Cianfrani, Francesco.

Title Canonical Quantum Gravity [electronic resource] : Fundamentals and Recent Developments

Published Singapore : World Scientific Publishing Company, 2014.


Location Call No. Status
Physical description 1 online resource (325 p.)
Notes Description based upon print version of record.
Contents Contents; Preface; List of Figures; List of Notations; 1. Introduction to General Relativity; 1.1 Parametric manifold representation; 1.2 Tensor formalism ; 1.3 Affine properties of the manifold; 1.3.1 Ordinary derivative; 1.3.2 Covariant derivative; 1.3.3 Properties of the affine connections; 1.4 Metric properties of the manifold; 1.4.1 Metric tensor; 1.4.2 Christoffel symbols; 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; 1.9.1 Levi-Civita construction
1.9.2 Algebraic properties and Bianchi identities1.10 Geodesic deviation; 1.11 Einstein's equations; 1.11.1 Equivalence Principle; 1.11.2 Theory requirements; 1.11.3 Field 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; 2.4.1 Universe critical parameters; 2.5 Inflationary paradigm; 2.5.1 Standard Model paradoxes; 2.5.2 Inflation mechanism; 2.5.3 Re-heating phase; 3. Constrained Hamiltonian Systems; 3.1 Preliminaries; 3.2 Constrained systems
3.2.1 Primary and secondary constraints3.2.2 First- and second-class constraints; 3.3 Canonical transformations; 3.3.1 Strongly canonical transformations; 3.3.2 Weakly canonical transformations; 3.3.3 Gauged canonical transformations; 3.4 Electromagnetic field; 3.4.1 Modified Lagrangian formulation; 3.4.2 Hamiltonian formulation; Conjugate momenta and primary constraints; Hamiltonian density; Secondary constraints; Constraints algebra; Tertiary constraint?; Equations of motion; 3.4.3 Gauge transformations; 3.4.4 Gauged canonicity
4. Lagrangian Formulations4.1 Metric representation; 4.1.1 Einstein-Hilbert formulation; 4.1.2 Stress-Energy tensor; 4.1.3 ΓΓ formulation; 4.1.4 Dirac formulation; 4.1.5 General f (R) Lagrangian densities; 4.1.6 Palatini formulation; 4.2 ADM formalism; 4.2.1 Spacetime foliation and extrinsic curvature; 4.2.2 Gauss-Codazzi equation; 4.2.3 ADM Lagrangian density; 4.3 Boundary terms; 4.3.1 Gibbons-York-Hawking boundary term; 4.3.2 Comparison among different formulations; 5. Quantization Methods; 5.1 Classical and quantum dynamics; 5.1.1 Dirac observables; 5.1.2 Poisson brackets and commutators
5.1.3 Schrödinger representation5.1.4 Heisenberg representation; 5.1.5 The Schrödinger equation; 5.1.6 Quantum to classical correspondence: Hamilton-Jacobi equation; Hamilton-Jacobi formalism; The WKB method; 5.1.7 Semi-classical states; Coherent states; Complexifier technique; The Ehrenfest theorem; 5.2 Weyl quantization; 5.2.1 Weyl systems; 5.2.2 The Stone-von Neumann uniqueness theorem; 5.3 GNS construction; 5.4 Polymer representation; 5.4.1 Difference operators versus differential operators; 5.4.2 The polymer representation of Quantum Mechanics
5.4.3 Kinematics
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-DeWitt equation, is fully discussed in order to outline its merits and limits. Afterwards, the reformulation of Canonical Quantum Gravity in terms of the Ashtekar-Barbero-Immirzi 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-DeWitt equation for the homogeneous Bianchi models and then by a detailed treatment of Loop Quantum Cosmology, including very recent developments. Contents: General Relativity; Quantization Methods; Classical and Quantum Geometrodynamics; Gravity as a Gauge Theory; Loop Quantum Gravity; Quantum Cosmology. Readership: Researchers in theoretical physics,
quantumphysics, general relativity and astrophysics.
Other author Ebook Library
Lecian, Orchidea Maria.
Lulli, Matteo.
Montani, Giovanni.
Subject General relativity (Physics).
Quantum gravity.
Electronic books.
ISBN 9789814556651 166.00 (NL)