Dynamics in canonical models of loop quantum gravity
arXiv:1910.00469
Abstract
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational field. The dynamics of the quantum states of the gravitational field is then generated directly by a physical Hamiltonian operator, instead of being implicitly defined through the kernel of a Hamiltonian constraint. We introduce a new construction of a Hamiltonian operator for loop quantum gravity, which has both mathematical and practical advantages in comparison to earlier proposals. Most importantly, the new Hamiltonian can be constructed as a symmetric operator, and is therefore a mathematically consistent candidate for a generator of physical time evolution in deparametrized models. We develop methods for approximately evaluating the dynamics generated by a given physical Hamiltonian, even if an exact solution to the eigenvalue problem of the Hamiltonian cannot be achieved. We also introduce a new representation for intertwiners in loop quantum gravity, based on projecting intertwiners onto coherent states of angular momentum, and in which intertwiners are represented as polynomials of certain complex variables, and operators in loop quantum gravity are expressed as differential operators acting on these variables. In addition to reviewing the results of the author's scientific work, this thesis also gives a thorough introduction to the basic framework of canonical loop quantum gravity, and a self-contained presentation of the graphical formalism for SU(2) recoupling theory, which is the invaluable tool for performing practical calculations in loop quantum gravity. The author therefore hopes that parts of this thesis could serve as a comprehensible source of information for anyone interested in learning the elements of loop quantum gravity.
arXiv commentPhD thesis. Faculty of Physics, University of Warsaw. 215 pages. A few minor corrections have been made relative to the refereed version of the work, which can be found at https://depotuw.ceon.pl/handle/item/3489. v2: More typos corrected. v3: Yet more typos fixed, and a couple of slight inaccuracies corrected in the presentation of the introductory material
References in corpus (63)
- The Dynamics of General Relativity
- Background Independent Quantum Gravity: A Status Report
- Discreteness of area and volume in quantum gravity
- Quantum Theory of Gravity I: Area Operators
- Real Ashtekar Variables for Lorentzian Signature Space-times
- Quantum Spin Dynamics (QSD)
- The Spin Foam Approach to Quantum Gravity
- Spin Networks and Quantum Gravity
- Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
- Dust as a Standard of Space and Time in Canonical Quantum Gravity
- Projective Techniques and Functional Integration
- A new spinfoam vertex for quantum gravity
- Partial observables
- Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
- Spin Network States in Gauge Theory
- The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
- Polyhedra in loop quantum gravity
- The physical hamiltonian in nonperturbative quantum gravity
- Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
- Time and a physical Hamiltonian for quantum gravity
- Representations of the Weyl Algebra in Quantum Geometry
- QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
- Towards Spinfoam Cosmology
- Closed formula for the matrix elements of the volume operator in canonical quantum gravity
- Gravity quantized
- Scalar Material Reference Systems and Loop Quantum Gravity
- Representation Theory of Analytic Holonomy C* Algebras
- Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time
- Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics
- Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity
- Volume and Quantizations
- Spectral Analysis of the Volume Operator in Loop Quantum Gravity
- Fast Radio Bursts and White Hole Signals
- The length operator in Loop Quantum Gravity
- Coherent spin-networks
- Quantum geometry from phase space reduction
- Quantum-Reduced Loop Gravity: Cosmology
- Emergent de Sitter epoch of the quantum Cosmos
- A new vacuum for Loop Quantum Gravity
- Operators for quantized directions
- Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
- Null dust in canonical gravity
- Cosmological constant in spinfoam cosmology
- Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint
- Smooth Big Bounce from Affine Quantization
- Quantum Reduced Loop Gravity: Semiclassical limit
- Gravitational Constraints which Generate a Lie Algebra
- Quantum evolution of black hole initial data sets: Foundations
- A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
- A curvature operator for LQG
- A symmetric scalar constraint for loop quantum gravity
- New Hamiltonian constraint operator for loop quantum gravity
- Towards Loop Quantum Supergravity (LQSG)
- Dynamical Quantum Geometry (DQG Programme)
- Quantum-Reduced Loop-Gravity: Relation with the Full Theory
- On loop quantum gravity kinematics with non-degenerate spatial background
- Matrix Elements of Lorentzian Hamiltonian Constraint in LQG
- A Homogeneous Model of Spinfoam Cosmology
- Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
- General relativity in the radial gauge: Reduced phase space and canonical structure
- Non-Abelian Stokes theorem in action
- Smooth Bounce in Affine Quantization of Bianchi I
- On the polymer quantization of connection theories: graph coherent states