Quantum Dyanmics of Loop Quantum Gravity
arXiv:0706.2623
Abstract
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, nonperturbative quantum theory for the Lorentzian gravitational field on a four-dimensional manifold. In this approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of "quantum Riemannian geometry", which is discrete at a fundamental scale. In the investigation of quantum dynamics, the classical expressions of constraints are quantized as operators. The quantum evolution is contained in the solutions of the quantum constraint equations. On the other hand, the semi-classical analysis has to be carried out in order to test the semiclassical limit of the quantum dynamics. In this thesis, the structure of the dynamical theory in loop quantum gravity is presented pedagogically. The outline is as follows: first we review the classical formalism of general relativity as a dynamical theory of connections. Then the kinematical Ashtekar-Isham-Lewandowski representation is introduced as a foundation of loop quantum gravity. We discuss the construction of a Hamiltonian constraint operator and the master constraint programme, for both the cases of pure gravity and matter field coupling. Finally, some strategies are discussed concerning testing the semiclassical limit of the quantum dynamics.
95 pages, MSc Thesis (Advisor: Dr. Jorge Pullin), Louisiana State University
References in corpus (65)
- The Confrontation between General Relativity and Experiment
- Background Independent Quantum Gravity: A Status Report
- Discreteness of area and volume in quantum gravity
- Quantum Nature of the Big Bang: Improved dynamics
- Quantum Theory of Gravity I: Area Operators
- Quantum Nature of the Big Bang
- Absence of Singularity in Loop Quantum Cosmology
- Logarithmic correction to the Bekenstein-Hawking entropy
- Black Hole Entropy from Loop Quantum Gravity
- Spin Networks and Quantum Gravity
- Spin Foam Models for Quantum Gravity
- Dust as a Standard of Space and Time in Canonical Quantum Gravity
- Quantum Gravity: a Progress Report
- Quantum geometry and the Schwarzschild singularity
- QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
- Weaving a classical geometry with quantum threads
- Projective Techniques and Functional Integration
- Partial observables
- Isolated Horizons: Hamiltonian Evolution and the First Law
- Does backreaction enforce the averaged null energy condition in semiclassical gravity?
- Representations of the holonomy algebras of gravity and non-Abelian gauge theories
- Black hole evaporation: A paradigm
- Differential Geometry on the Space of Connections via Graphs and Projective Limits
- Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
- Fundamental Structure of Loop Quantum Gravity
- The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
- Quantum Spin Dynamics (QSD) II
- Geometry of Generic Isolated Horizons
- Actions for Gravity, with Generalizations: A Review
- The physical hamiltonian in nonperturbative quantum gravity
- Inflation from Quantum Geometry
- Graviton propagator from background-independent quantum gravity
- Disappearance of Black Hole Singularity in Quantum Gravity
- Physical effects of the Immirzi parameter
- QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
- The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
- Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
- Spherically Symmetric Quantum Geometry: States and Basic Operators
- Loop Quantum Gravity: An Inside View
- On the Renormalization Group in Curved Spacetime
- Gauge Field Theory Coherent States (GCS) : IV. Infinite Tensor Product and Thermodynamical Limit
- A black hole mass threshold from non-singular quantum gravitational collapse
- QSD IV : 2+1 Euclidean Quantum Gravity as a model to test 3+1 Lorentzian Quantum Gravity
- Dynamical Initial Conditions in Quantum Cosmology
- Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
- On the regularization ambiguities in loop quantum gravity
- Spin foam model for Lorentzian General Relativity
- QSD VI : Quantum Poincaré Algebra and a Quantum Positivity of Energy Theorem for Canonical Quantum Gravity
- Spacetime states and covariant quantum theory
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
- Nonsingular Black Holes and Degrees of Freedom in Quantum Gravity
- Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
- Semiclassical States for Constrained Systems
- Testing the Master Constraint Programme for Loop Quantum Gravity IV. Free Field Theories
- Initial Conditions for a Universe
- Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
- Gravitons from a loop representation of linearised gravity
- Master Constraint Operator in Loop Quantum Gravity
- Consistent discretization and loop quantum geometry
- Elements of Loop Quantum Cosmology
- Loop Quantum Gravity on Non-Compact Spaces
- operator for canonical quantum gravity
- Quantum Gravitational Collapse
- Classical Geometry from a Physical State in Canonical Quantum Gravity