Testing the Master Constraint Programme for Loop Quantum Gravity IV. Free Field Theories

Abstract

This is the fourth paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. We now move on to free field theories with constraints, namely Maxwell theory and linearized gravity. Since the Master constraint involves squares of constraint operator valued distributions, one has to be very careful in doing that and we will see that the full flexibility of the Master Constraint Programme must be exploited in order to arrive at sensible results.

23 pages, no figures

References in corpus (32)

• Background Independent Quantum Gravity: A Status Report
• Quantum Spin Dynamics (QSD)
• Loop Quantum Gravity
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Lectures on Loop Quantum Gravity
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Quantum Spin Dynamics (QSD) II
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
• QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
• Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
• An invitation to loop quantum gravity
• Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
• Gauge Field Theory Coherent States (GCS) : IV. Infinite Tensor Product and Thermodynamical Limit
• QSD IV : 2+1 Euclidean Quantum Gravity as a model to test 3+1 Lorentzian Quantum Gravity
• Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
• Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
• Gravitons and Loops
• QSD VI : Quantum Poincaré Algebra and a Quantum Positivity of Energy Theorem for Canonical Quantum Gravity
• Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme
• Towards the QFT on Curved Spacetime Limit of QGR. II: A Concrete Implementation
• Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
• Diffeomorphism covariant representations of the holonomy-flux star-algebra
• On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories
• Generalized boundary conditions for general relativity for the asymptotically flat case in terms of Ashtekar's variables
• Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
• Universal Procedure for Enforcing Quantum Constraints
• Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models
• On the Implementation of Constraints through Projection Operators

Cited by in corpus (39)

• Partial and Complete Observables for Canonical General Relativity
• Fundamental Structure of Loop Quantum Gravity
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Reduced Phase Space Quantization and Dirac Observables
• Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
• Loop quantization of spherically symmetric midi-superspaces
• Quantum Spin Dynamics VIII. The Master Constraint
• (Broken) Gauge Symmetries and Constraints in Regge Calculus
• A perturbative approach to Dirac observables and their space-time algebra
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
• On (Cosmological) Singularity Avoidance in Loop Quantum Gravity
• Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
• Uniform discretizations: a new approach for the quantization of totally constrained systems
• Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
• Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models
• The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
• Master Constraint Operator in Loop Quantum Gravity
• From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
• An elementary introduction to loop quantum gravity
• Three Dimensional Loop Quantum Gravity: Particles and the Quantum Double
• Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
• Observations on interfacing loop quantum gravity with cosmology
• On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition
• Emergent diffeomorphism invariance in a discrete loop quantum gravity model
• A gravitationally induced decoherence model using Ashtekar variables
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Hamiltonian Renormalisation V: Free Vector Bosons
• A Path-integral for the Master Constraint of Loop Quantum Gravity
• Linearized Quantum Gravity Using the Projection Operator Formalism
• Approximating the physical inner product of Loop Quantum Cosmology
• Loop quantum gravity - a short review
• The SL(2,R) totally constrained model: three quantization approaches
• Quantum Dyanmics of Loop Quantum Gravity